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SYMBOLISM AND TRUTH 


LONDON : HUMPHREY MILFORD 


OXFORD UNIVERSITY PRESS 






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SYMBOLISM AND TRUT 


AN INTRODUCTION TO 
THE THEORY OF KNOWLEDGE 







BY 


RALPH MONROE iene ibe. D: 


INSTRUCTOR AND TUTOR IN PHILOSOPHY 
HARVARD UNIVERSITY 





CAMBRIDGE 
HARVARD UNIVERSITY PRESS 


1925 


COPYRIGHT, 1925 


BY HARVARD UNIVERSITY PRESS 


PRINTED AT THE HARVARD UNIVERSITY PRESS 


CAMBRIDGE, MASS., U.S. A. 


TO 


. B. €. 


IN GRATITUDE FOR 
FAITH AND WORKS 


When I heard the learn’d astronomer; 

When the proofs, the figures, were ranged in columns before me; 

When I was shown the charts and the diagrams, to add, divide, 
and measure them; 

When I, sitting, heard the astronomer, where he lectured with 
much applause in the lecture-room, 

How soon, unaccountable, I became tired and sick; 

Till rising and gliding out, I wander’d off by myself, 

In the mystical moist night-air, and from time to time, 

Look’d up in perfect silence at the stars. 


Wait Wuitman, Drum Taps, 1865 


PREFACE 


Tue theory of knowledge, occupying as it does the borderland 
between psychology, logic, and metaphysics, is a peculiarly diffi- 
cult subject to isolate and study in itself. The materials are 
widely scattered through philosophical literature, discussions of 
the problems appear in works of the most diverse character, and 
any one who attempts to single out the essential questions will 
be sure to omit some that are important in the eyes of many 
people and to include others that might be omitted. He will 
place his emphasis somewhere, with the result that he will fail to 
stress points that perhaps equally deserve emphasis. By way of 
remedy therefore he ought to indicate his angle of approach and 
call attention to what he believes are the major gaps in his treat- 
ment. 

The method of the present work is mainly critical and ana- 
lytic, rather than speculative.’ A single line of attack, which 
goes at once to the heart of the problem, is chosen—namely, the 
réle of symbols in knowledge; and about this the entire analysis 
is organized. Knowledge is inseparable from its expressions; a 
study of these expressions should therefore throw light on the 
theory of knowledge as a whole. With this conviction, I begin by 
examining meaning. But unfortunately the psychology of mean- 
ing is still in a fluid state, and the most that one who is not a 
psychologist can do is to point out in a rough way that to which, 
in his own experience, he gives the name “meaning.” The con- 
sideration of the logical forms of meanings leads to a discussion 
of the nature of facts, relations, qualities, universals and indi- 


1 See Mr. C. D. Broad’s interesting statement of the difference between 
critical and speculative philosophy in Contemporary British Philosophy, edited 
by Professor J. H. Muirhead (1924), pp. 63 ff.; also, Broad’s Scientific Thought, 
(1923), introduction. 


Vill PREFACE 


viduals, classes, description, synthesis and analysis, possibility, 
and finally to the definition and tests of truth. The question of 
truth is naturally linked to that of belief, judgment, and nega- 
tion; and since logical form stands out most clearly in quasi- 
mathematical deductive systems, a chapter is given to the study 
of these systems. 

Metaphysical ideas are kept as far as possible in the back- 
ground. Speculations concerning the relation of knowledge to an 
ultimate reality, that is, the issues of idealism and realism, of 
gnosticism and agnosticism, of monism and pluralism, of the 
final validity of intuition as opposed to reason, are postponed 
until the last chapter; for a theory of the relation of knowledge 
to reality can be successfully held only after the ground has been 
cleared by an analysis of knowledge as a phenomenon. By exam- 
ining in detail the elements that make up the complex process, 
knowledge, I hope to introduce the reader to the wider specu- 
lative aspects of the subject; but in this direction the line of 
further thought is merely sketched. 

Discussions of the theory of knowledge often begin by classi- 
fying different types of views and proceed to compare these in 
the effort to distill some truth from each. This method is useful; 
it sets in order, for one unfamiliar with philosophy, a large 
amount of material; but it tends to become a study of conflict- 
ing schools of opinion on the problem of knowledge rather than 
of the problem itself. No systematic classification of epistemo- 
logical theories is given here, though an acquaintance with such 
classifications, and with the history of philosophy, will be help- 
ful to the reader. 

The central place of the concept of logical form gives to cer- 
tain parts of the book a superficial resemblance to Mr. L. Witt- 
genstein’s recent T'ractatus Logico-Philosophicus. How deep this 
resemblance goes I am unable to say, but the language is similar. 
“We make to ourselves (in thought) pictures of facts,” says Mr. 


PREFACE IX 


Wittgenstein. ‘‘In the picture and the pictured there must be 
something identical in order that the one can be a picture of the 
other at all. What the picture must have in common with the 
reality in order to be able to represent it after its manner — 
rightly or falsely —is its form of representation.”’ And Mr. 
Bertrand Russell adds to this the comment, “‘We speak of a 
logical picture of a reality when we wish to imply only so much 
resemblance as is essential to its being a picture in any sense, 
that is to say, when we wish to imply no more than an identity 
of logical form.” 4 

The positive or descriptive theory of knowledge of the first 
seven chapters, which attempts cautiously to thread its way be- 
tween psychology and metaphysics, is no doubt allied to the 
type of philosophy known in Germany as phénomenologie. But 
it leans much more heavily towards psychology than does the 
phinomenologie of E. Husserl’s Logische Untersuchungen. Simi- 
larly, A. Meinong’s theory of the objective, set forth in his Unter- 
suchungen zur Gegenstandstheorte und Psychologie, in his studies 
of Hume and other works, appears to me to remove meaning too 
completely from its psychological setting and to view as simple 
what is in reality complex. However, I am at one with the phe- 
nomenological school in wishing to treat the theory of knowl- 
edge as an autonomous subject, that is, in desiring to assure it 
as much autonomy as belongs to any other branch of philosophy 
or to psychology. It is clear that knowledge cannot be wholly 
described in psychological terms. Hume attempted this and 
failed. But it is clear also that nothing is gained by trying to 
banish from knowledge all concrete psychological factors. 

Among the topics that might be included in such a critical 
study of knowledge but that are omitted or only lightly touched 
here, are the following: the knowledge of other minds and of the 


1L. Wittgenstein, Tractatus Logico-Philosophicus (1922), introduction, 
p. 10. 


x PREFACE 


self; the knowledge of values and the relations of theories of 
truth to theories of moral and aesthetic value; the validity of in- 
ductive inferences; the nature of scientific hypotheses, especially 
the place of elegance, economy, and completeness in scientific 
theories; the knowledge of space and time. (The allusions to 
space and time made in connection with the discussion of the in- 
dividual in Chapter III need to be supplemented by a detailed 
treatment, such as that of Mr. A. N. Whitehead’s The Principles 
of Natural Knowledge and Mr. C. D. Broad’s Scientific Thought. 
Particularly is this so at the present time, in view of the theory 
of relativity.) But what is said here of the fundamental factors 
in knowledge may suggest ways of approach to these more 
tangled problems. 

For the use of the student, a list of selected readings bearing 
on the subjects discussed in each chapter is given. This makes 
‘available for study along with the text some of the widely scat- 
tered literature of the theory of knowledge, and will aid the stu- 
dent in obtaining a complete and systematic grasp of this branch 

of philosophy. 
R. M. E. 


CAMBRIDGE, Mass. 
January, 1925. 


CONTENTS 


INTRODUCTION Sods daybed ia SO AIO Og cle 
1. The point of view of the theory of knowledge. —2. The positive 
theory of knowledge distinguished from the metaphysics of knowledge. 


CHAPTER I 


1. Two senses of the term idea: idea and image. Images not the only ele- 
ments of knowledge. — 2. Images do not mean by resemblance alone. Sym- 
bols may mean any kind of objects; not restricted to meaning images or the 
present content of the mind. — 3. Mediate and immediate knowledge. Im- 
mediate knowledge the presentation of objects, mediate knowledge represen- 
tation through symbols. — 4. Presentation as a union of sensation and 
conception: sensations as signs. The passage from presentation to represen- 
tation. —5. Pure awareness: not the apprehension of sense data. A non-con- 
ceptual cognition of the real. — 6. Meaning a function of psychical activity: 
not the association of ideas. —'7. The meaning activity as preparation for 
an object. Overt action as a sign of belief. Belief and understanding. — 8. 
The behavioristic analysis of meaning inadequate: does not distinguish 
habits of meaning from other habits. The meaning activity a suspension of 
outward action, and hence observable only in introspection. — 9. Summary 
of the description of meaning. The nature of thought in general. — 10. Syn- 
tactical meaning: a complex meaning is a synthesis of meanings in a single 
meaning and represents an object or fact analytically, that is, as a unity of 
elements. — 11. Simple symbols: unless their meanings are defined they 
have significance only through reference to experienced objects. Simple 
symbols an integral part of presentations. — 12. Syntactical meanings 
built on simple meanings. A group of symbols may be significant when there 
is no object to which it refers. — 13. Summary. 


CHAPTER II 


AMMEN Sey Te ae aan Vax Se) Dama ERR eae oi 


1. Symbolic groups as copies of the logical form of complex objects: their 
likeness to maps. — 2. Logical form determined by characters and relations 
which belong to objects as such. Symbols being objects share these with the 
things they mean. — 3. The concept of growping: the same as the concept 
of function. Demands that the whole be uniquely determined by its parts, 
and the meaning of a symbolic whole by the meanings of its parts. Symbols 
reproduce factual groups by symbolic groups. — 4. Numerical identity and 
diversity as formal characters of objects. These together with grouping de- 
termine the form of symbols and of facts. Simple symbols not formally dis- 
tinct; they set the scale of representation. Groups differ formally in multi- 


xii 


CONTENTS 


plicity, or type, or both. — 5. Signs of syntax: symbols of symbolism. A gen- 
eral schematism for presenting logical forms. Comparisons of form effected 
by one-to-one correlations. — 6. Alternative analyses of identical objects. 
Statements of identity not trivial. — 7. The principle of identity: two in- 
terpretations — as a principle of symbolism and as a statement of fact. 
Equivalences by definition. — 8. The third distinguishing feature of logical 
form: the distribution of tautologous symbols or identical elements within 
groups. — 9. Summary. 


CHAPTER III 


UNIVERSALS AND INDIVIDUALS: ORDER 


1. The objects of knowledge are of double aspect: iniveal Aa; individual. 
— 2. The antinomy of the universal and the individual: no description 
reaches the specific essence of the individual. — 3. Spatial and temporal 
relations do not determine individuals. — 4. The postulate of the identity 
of indiscernibles: leaves the antinomy of the universal and individual un- 
solved for finite knowledge. — 5. Representation of the individual through 
a variable: the variability of proper names. — 6. Universals determinately 
known: as identities in changing and diverse instances. —7. The struc- 
tural function of universals: elements of unity in facts. The distinction be- 
tween terms and elements of unity. The unity of fact indefinable. — 8. The 
structural function of individuals: they appear only as terms. — 9. Uni- 
versals as terms: abstraction, beginning in perception and completed in con- 
ception. — 10. The objectivity of universals: arguments against nominal- 
ism. — 11. A grammar of symbolism based on the distinction between terms 
and elements of unity. — 12. Plans of syntax in symbolic systems as deter- 
mining possibilities for knowledge. Deductive and non-deductive systems. 
— 13. Nonsense: distinguished from fantasy, absurdity, and contradiction. 
— 14. Order described in terms of group structure. Asymmetry. — 15. 
Symmetry: symmetrical relations as relations without sense. — 16. Repre- 
sentations of order through spatially and temporally ordered symbols am- 
biguous. — 17. Complex elements of unity. — 18. Summary. 


CHAPTER IV 


DESCRIPTION AND ANALYSIS 


1. General nature of descriptions: Votes euiee to terms through predicates of 
these terms. — 2. Descriptions mean complex wholes: in this respect they 
are like propositions. — 3. Descriptions distinguished from other complex 
expressions by their form: through a variable they signify a term as modi- 
fied by a predicate; the term takes a central, rather than a subordinate 
place, in the structure. — 4. The variable: variable meaning a distinct kind 
of significance attaching to an uninterpreted element in a whole. A minimal 
context of logical structure necessary to variables. — 5. The ambiguity of 
the variable: distinguished from equivocation. Variable meanings must 
follow the principle of identity. “The,” “a,” “any,” and “‘some,”’ as signs 
of interpretation. — 6. Descriptions of universals. —7. Examination of 
Messrs. Russell and Whitehead’s argument, from the triviality or falsity of 
“Scott is the Author of Waverley,” to prove that descriptions are incomplete 


66 


108 


CONTENTS xiil 


symbols. Such statements neither trivial nor false. —8. Judgments of 
analytic form and synthetic effect: they analyze unanalyzed concepts or en- 
large the meanings of concepts. — 9. Indeterminateness of proper names. — 
10. Judgments of synthetic form and analytic effect. — 11. Knowledge in 
universal terms determinate. The tendency of science to become analytic in 
form: a completely interpreted science rests on some synthetic judgments.— 
12. Descriptions of the non-existent: the significant use of symbols when 
they refer to no objects. The theory of descriptions as incomplete symbols 
rests on a narrow conception of meaning. —13. Classes: not the same type 
of objects as facts. Defined through the primitive idea of totality. — 14. 
Summary. 


CHAPTER V 


LECPaPANDMOALSIT Ly hl chch ae em enue Uae kU TAQ 
1. Truth and falsity as properties of symbols. Meaning both necessary and 
sufficient to truth. Truth and reality. — 2. Examination of the theory that 
truth is a property of subsistent entities or propositions. The proposition as 
a tertium quid. — 3. The objective reference of meanings independent of the 
existence or subsistence of a referent. — 4. Subsistent entities not necessary 
to the analysis of meaning. Propositions as symbols. — 5. Perception as a 
criterion of existence. Conceptual constituents in perception. Dreams, 
illusions, hallucinations. Bare existence alone guaranteed by givenness in 
perception. — 6. Sensationalism and empiricism contrasted: sense data 
not the only data. Presentational thinking as a means of knowing the real. 
The tabula rasa view of mind. —7. Consistency with the whole of knowl- 
edge as a criterion of existence. Rationalism and irrationalism: limited 
rationalism. — 8. The empirical categories. Theory and perception as 
mutually corrective. —9. Tests of truth: distinguished from truth. — 
10. The coherence theory. Truth as correspondence implies the distinct- 
ness of knowledge and reality. Identity of logical form the medium of corre- 
spondence. — 11. Belief, judgment, and assertion. Belief continuous with 
understanding. The interest in truth as the motive of belief. Pure specula- 
tion. — 12. Belief not the addition of the concept of existence: the onto- 
logical argument. Single words and incomplete phrases as propositions. — 
13. Disbelief as belief in negative propositions. Incredulity or scepticism 
the true opposite of belief. — 14. Signs of belief: the copula. — 15. Rela- 
tivism and scepticism. The need for belief. The concept of truth as an ap- 
proach to metaphysics. — 16. Summary. 


CHAPTER VI 


NEGATION AND CONTRADICTION .............. 197 


1. The paradox of negative truth: negative facts. The negative as a vari- 
able. — 2. Ambiguity essential to negation: the possible values of a nega- 
tive as its possible grounds. Incompatibility of propositions not a part of 
the definition of the most elementary sort of negation. Formal and material 
simplicity of concepts. — 3. Purely conceptual negation: the possible values 
of the negative determined by distinctness of meaning irrespective of ob- 


X1V 


Format DEDUCTION ..... 


CONTENTS 


jects meant. “Determination is negation.” — 4. The principles of identity 
and contradiction as general rules of symbolism, and as general conditions 
of the being of objects. — 5. The law of the excluded middle: the inferential 
negative. — 6. The conditions of the truth and falsity of negatives. Am- 
biguous truth. The implications of the law of the excluded middle. — 
7. Negative judgments: bare denial contrasted with specific denial. — 8. 
Conceptual validity and truth: formal and material consistency. — 9. Sum- 
mary. 


CHAPTER VII 


1. The study of pure form through uninterpreted symbols: sets of postu- 
lates as plans of syntax. — 2. The general principles of symbolism: assumed 
in all deductive systems. — 3. Substitution as the modus operandi of formal 
deduction. The rule of completeness of substitution. Equations of struc- 
ture. Implicational substitutions. — 4. An uninterpreted Boolean Algebra 
as an illustration of formal deduction. — 5. The class interpretation of the 
Boolean Algebra. — 6. The meaning of rules of substitution: ranges of 
variability : functional constants and functional variables. — 7. Operations 
distinguished from relations. A set of postulates for serial order. — 8. In- 
ference: its relation to belief and assertion. Completely interpreted deduc- 
tive systems completely inferential. — 9. Incompletely inferential systems: 
analogy between the manipulations of a formal deductive system and the 
thought process in words and images. Reason and imagination. — 10. Sum- 
mary. 


CHAPTER VIII 


THe METAPHYSICS OF KNOWLEDGE .. 


1. Metaphysical basis of criticisms of knowledge. Scepticism and meta- 
physics. — 2. Critical agnosticism. Kant and Locke. — 3. The theory of 
mind-isolation in Kant and Locke. — 4. Positive conclusions from the re- 
jection of agnosticism. — 5. Appearance and reality: how this distinction 
must be interpreted. — 6. The relation of the mind to real objects in cog- 
nition: activity and passivity in knowledge. Idealism. — 7. Critique of 
idealism. Materialism. — 8. Neutralism. The mental and the physical as 
aspects of reality. —9. The mental and the physical discovered within a 
single field of experience. Mind and non-mental objects continuous in cog- 
nition; specific nature of this continuity. — 10. The problem of the cogni- 
tion of physical objects distinguished from the mind-body problem. The 
relevance of perceptual objects to the psycho-physical situation. — 11. The 
role of thought-activity in knowledge: the general as fulfilling the intentions 
of thought. Innate ideas. — 12. Is reality logical in form? Intuition and ir- 
rationalism. — 13. Metaphysical insight. The relation between the form 
and the detail of reality. A final truth in a growing experience. — 14. Con- 
clusion. 


SUPPLEMENTARY READINGS 


INDEX 


. 222 


266 


317 
323 


SYMBOLISM AND TRUTH 









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INTRODUCTION 


I 


As the various sciences have branched off from the common 
stem of philosophy, which was in the beginning the pursuit of 
truth wherever it might be found, the philosophers have been 
left with certain problems preéminently their own, and among 
these is the theory of knowledge. It is not probable that the 
theory of knowledge will ever be a science in the sense in which 
mathematics, physics, and biology are sciences. There is too 
much room for difference of opinion, not only in the solution of 
its problems, but in their statement. Yet progress in this field of 
thought, as in any other, comes only with the attempt to define 
the subject-matter more clearly, to cut it off from neighboring 
fields which threaten it with incursions of irrelevant questions, 
and to find some ideas that bind the whole together. 

Just as a physical theory takes its rise from physical facts, so 
a theory of knowledge is built on the facts of knowledge; but 
though these facts are before us when we make the simplest 
statement or perform the most elementary process of reasoning, 
they are by no means so apt to strike the mind as are the facts of 
physics or of any other special science. We are mentally far- 
sighted and tend to neglect that which is closest to us. 

Everything that can be mentioned is known in some sense. If 
I deny the existence of two-headed lions or red elephants, I 
know what I mean by these denials, and therefore these imagi- 
nary creatures are somehow objects of my knowledge. If I open 
my eyes on the world about me, I see trees and houses, and 
people passing in the street; and these are obviously known in 
some other way than the red elephants and the two-headed 
lions. The geometer sketches a rough triangle on a bit of note- 


4 SYMBOLISM AND TRUTH 


paper, and on this diagram demonstrates that the sum of the 
three interior angles of the triangle is equal to a straight angle. 
This exact geometrical proposition is not true of the imperfect 
penciled triangle; it is true of an ideal Platonic triangle, which is 
only suggested by the rough figure and is apprehended through 
the eye of reason rather than the eye of sense. The ideal triangle 
belongs thus to another class of objects of knowledge, just as do 
the ideal gas, the frictionless motion, the perfectly rigid and 
elastic body, of the physicists. Again, what is one to say of 
dream objects? The events and people of dreams are for the 
time as intensely real as the events and people in the street out- 
side at the present moment. What is the reason for our prejudice 
in favor of the reality of the things of waking life, which fill at 
best only three-quarters of our experience? Certainly the dream 
is a form of knowledge. 

There are evidently many different senses of the term ‘‘knowl- 
edge.’ We dwell in the medium of the known, which surrounds 
us as an atmosphere. This very ubiquity makes it difficult to 
stand off from knowledge and analyze it. Perhaps the simplest 
way of marking out the subject-matter of the theory of knowl- 
edge is this: Anything of which it can be said that it is known in 
any sense is a proper subject of our investigation. The theory of 
knowledge is interested in these things not as physical, psycho- 
logical, mathematical, or any other particular sort of objects, 
but as things known. Although mathematical equations, physi- 
cal, chemical, and biological laws, historical facts, and a multi- 
tude of other data which belong to the special sciences are also 
data of the theory of knowledge, this theory looks on them in a 
different light from any of the special sciences. What common 
factors, laws, uniformities, relations, belong to things merely as 
objects of knowledge? This is the question that must be asked. 

Thus the theory comprehends in its subject-matter all the 
special sciences. These are particular cases of knowledge from 


—— 


INTRODUCTION 5 


which the general principles are to be induced. But it attacks 
problems that none of these sciences can meet. With Bacon it 
“takes all knowledge to be its province” and views this province 
from an angle of its own. It includes much of what is often classi- 
fied as philosophy of science or logic, for it considers such ques- 
tions as what is a proposition, what is a scientific law, what are 
truth, error, assertion, belief, conception, meaning? In short, 
wherever there are principles of the known qua known, these 
principles are a part of the theory of knowledge. 

Meaning, for example, is present in all knowledge, from the 
simplest perception to the most complex mathematical expres- 
sion. Any knowledge that does not make use of meaning is an 
immediate awareness, an intuition, which can give no rational 
account of itself. Just what meaning is is a thorny question. But 
if a satisfactory answer can be given, the description of knowl- 
edge will have been pushed forward some distance. Moreover, 
one of the most notable facts about knowledge — and this is 
plainly connected with the presence of meaning — is that it can 
be expressed. Knowledge can be shut in between the covers of 
books and passed on from generation to generation; it can be 
transmitted from mind to mind by word of mouth; it can be em- 
bodied in the intricate formulae of the exact sciences. The sym- 
bols which are the outward instruments of this expression must 
have a close and necessary relation to the thought they convey, 
and the analysis of these instruments should aid us in bringing 
the true nature of knowledge into view. It is from this angle that 
we propose to attack the problem. 


II 


The most troublesome intruder in the field of the theory of 
knowledge is metaphysics, for the questions that usually first 
suggest themselves to the student of the subject are these: How 
is knowledge related to reality? Is reality independent of or de- 


6 SYMBOLISM AND TRUTH 


pendent on knowledge? Is it genuinely given in knowledge, and 
if so how? These questions turn on the distinction of subject and 
object, of a knowing-being with ideas, perceptions, and sensa- 
tions, and an external world of existences alien to this being. Is 
this alienation complete? Or is there a rapprochement between 
reality and the mind in which it makes its appearance? Many 
philosophers believe that before a theory of knowledge can be 
stated these problems must be solved. 

But if this were so, it would be as if the physicist insisted that 
a theory of the ultimate nature of mass is essential to a state- 
ment of the laws of mechanics, or as if the biologist refused to 
examine the laws of heredity without an adequate definition of 
life. Human knowledge is a fact just as mass, motion, and life 
are facts. The study of its principles, its elements, its structure, 
does not presuppose an answer to the more ultimate questions, 
how is this fact possible? — what is the relation of knowledge to 
reality? These queries carry one beyond the analysis of knowl- 
edge itself to a theory of reality, and no one can hope to discover 
whether or not reality is reached through knowledge until he 
knows what knowledge is. 

Though none of these metaphysical questions is prior to the 
descriptive study of knowledge, no theory would be complete 
unless it attempted to answer them. A good theory — of any- 
thing — must consider all the intelligible questions its data sug- 
gest; and so a complete theory of knowledge will fall into two 
parts: it will be both a positive analysis and a metaphysics of 
knowledge, it will both describe knowledge and explain its rela- 
tion to reality. But the metaphysics of knowledge demands a 
final concept of reality, and it naturally supervenes on a more 
restricted inquiry which makes use of a provisional, working 
concept of the real. Let us call this the posttwe theory of knowl- 
edge, epistemology proper, which is an examination of knowledge 
undertaken in the spirit of the laboratory. We must begin by 





INTRODUCTION 7 


viewing knowledge as a natural phenomenon if we are to deter- 
mine its place in reality. We must proceed inductively and “‘rise 
by gradual steps to that which is prior and better known in the 
order of nature,” instead of ‘‘beginning at once by establishing 
certain abstract generalities.” ! 

From the point of view of the positive theory of knowledge 
one can set out without being a realist, an idealist, a monist, a 
pluralist, a nominalist — without attaching himself to any sys- 
tem of metaphysics. Metaphysics comes later; it is the coping- 
stone of the theory and it cannot be securely placed without a 
careful survey of the facts. 

The confusion of metaphysics with the positive analysis of 
knowledge can be traced, in modern thought, to Locke. Locke’s 
Essay, though it deals with the structure and laws of knowledge, 
especially with the manner in which ideas are built up from sim- 
ple impressions into complex systems, is nevertheless shot 
through with the conception of an unknowable substance which 
lies beyond ideas. This conception colors the whole work. For 
Berkeley and Kant, metaphysics is still intertwined with the 
descriptive treatment of knowledge, though the Critique of Pure 
Reason in distinguishing the transcendental aesthetic and analytic 
from the dialectic makes a division that corresponds roughly to 
these two aspects of the subject. Yet the whole Critique is 
haunted by a metaphysical ghost — the thing-in-itself. The 
first modern philosopher who severely restricts himself to the 
analysis of knowledge without metaphysics is Hume, and this is 
accidental, the result of his scepticism. Since he believed in no 
theory of reality, he advanced no theory of the relation of 
knowledge to reality, but he fell on the contrary into the trap of 
the purely psychological point of view. 

The phdénomenologie which has become prominent in recent 
German philosophy, especially through the writings of A. 


1 F. Bacon, Novum Organum, Bk. I, Aphorism 22. 


8 SYMBOLISM AND TRUTH 


Meinong and E. Husserl, pursues the analysis of knowledge in 
the positive spirit; and the same tendency, if not the same mat- 
ter, is to be found in England in the work of Mr. Bertrand 
Russell, Mr. A. N. Whitehead, Mr. G. E. Moore, and Mr. C. D. 
Broad. 

Yet metaphysics always lurks in the background, even for 
those who attempt to avoid this type of speculation. The ques- 
tion of the ultimate validity of knowledge remains to be an- 
swered; the notion of truth points inevitably to a final concept 
of the real. A definition of truth cannot fail to invite metaphysi- 
cal criticism, and it can be defended in the last resort only by 
arguments that rest on metaphysical premises. Therefore, un- 
less we are to persist in a partial scepticism such as Hume’s, the 
separation of the positive theory of knowledge from metaphys- 
ics cannot be maintained to the end; but it is of immense value 
as a working distinction in the study of epistemology. 








CHAPTER I 


MEANING 
I 


Wuavr are the facts that a theory of knowledge needs to organ- 
ize and explain? 

It is customary to say that knowledge is built up from ideas. 
Locke defined knowledge as “‘nothing but the perception of the 
connection of and agreement, or disagreement and repugnancy, 
of any of our ideas,”’ and he gave as his reason for this definition 
that “‘the mind, in all its thoughts and reasonings, hath no 
other immediate object but its own ideas, which it alone does or 
can contemplate.” ! If we ask what ideas are, we learn nothing 
more definite than that they are the mind’s objects. Thus 
Locke’s statement that “‘our knowledge is conversant only with 
ideas” affirms that knowledge is conversant only with the 
mind’s objects — a truism which no one will deny. The term 
“idea” is robbed of its force by being extended to all the ele- 
ments of knowledge. 

There is a narrower and more profitable sense of this term, 
which makes ideas one class of the ingredients of knowledge, but 
not the only class. This is the sense in which “idea” is used by 
the psychologist. An idea is an image, a psychical event, and 
it must be distinguished from other psychical events, namely 
sensations and perceptions. The ground of this distinction is 
difficult to establish. Intrinsically an image and a sensation or 
perception are much the same. The difference is not, as Hume 
supposed, one of vividness or intensity. But the things of sen- 
sation and perception have a type of coherence with one another 


1 J. Locke, Essay Concerning Human Understanding, Bk. IV, ch. i, secs. 1, 2. 


10 SYMBOLISM AND TRUTH 


which those of the imagination do not have. Sensory and per- 
ceptual objects obey, not merely “psychical” laws, but also the 
laws of physics; and so in most cases images can be set apart 
from sensations and perceptions. 

The striking thing about ideas in this narrower sense is that 
they usually refer beyond themselves to other things. They are 
not as a rule self-contained, but reach out with tentacles of sig- 
nificance toward other ideas or toward the things of sensation 
and perception. Locke found this to be characteristic of all 
ideas in his sense of the term, that is, of all the mind’s objects. 
They are all symbolic of that which lies beyond the mind’s 
grasp, says Locke. But since the realities which these ideas sig- 
nify are not themselves ideas, Locke is at a loss to interpret the 
meaning of knowledge in terms of these extra-mental realities. 
He is clear however on one point, that ideas in so far as they are 
vehicles of knowledge are symbolic; that the area of knowledge 
is coextensive with the area of significance. 

In the more restricted sense of “‘idea,”’ it is not necessary to 
attempt the impossible, to seek beyond knowledge for the mean- 
ing of ideas. They are to be interpreted as referring to objects 
sensed or perceived, and often as referring to other ideas or psy- 
chical states. But as mere meaningless successions of psychical 
phenomena following the laws of association, ideas (images) are 
of no special importance in knowledge; they are not conveyors 
of knowledge. They make their appearance before the mind and 
pass away, and this is all that can be said about them. However, 
as mediators between the mind and objects in perception or ob- 
jects beyond the immediate circle of the mind—in other words, 
as significant symbols— images are the first instruments of 
meaning and hence of knowledge. Instead of saying as Locke 
does that “knowledge is of ideas,” one ought rather to say that 
knowledge comes through ideas. It would be of slight value to 
have knowledge of ideas if we did not know through ideas. 


MEANING 1] 


Images, then, pass by the easiest possible transition to a 
second level of knowledge, the level of significance. Without 
perceptible effort, the mind takes them to refer to something 
other than themselves, and thus endows them with a function 
which attaches much less readily to other elements of knowledge 
— the function of meaning. 


II 


What do images signify? The simplest answer is that they sig- 
nify things they resemble. Though this is true in many in- 
stances, and is indeed the reason why they are such ready 
vehicles of meaning, images are not restricted in their signifi- 
cance to the objects of which they seem to be faint and partial 
copies. The vagaries of individual processes of imagery are with- 
out limit, and therefore naive copy theories of the significance of 
ideas are faulty. The subtlety of the threads that bind ideas to 
their objects must be recognized. Any image may come to mean 
any object. 

The fact that images resemble the experiences which pro- 
duced them, and that the image of a part of an experience tends 
to recall the whole, so that they take on meaning with a mini- 
mum of effort on our part, makes images the primal instruments 
of knowledge. But they are not the only instruments. Man adds 
to them and improves on them. He adds speech and writing, and 
finally the complex symbols of mathematics and logic. Ideas 
take their place as one among many classes of symbols. 

It is no doubt possible completely to supplant images as vehi- 
cles of thought by words or other conventional signs. Yet, when 
the major burden of significance is carried by symbols other 
than images, the latter usually arise in the process. In most 
minds significant imagery is never wholly absent. The traces of 
our intellectual childhood, when to think of things is to see them 
vividly in imagination, remain with us in the most abstract 


12 SYMBOLISM AND TRUTH 


kinds of thought. Witness the many attempts to visualize Ein- 
stein’s “spherical universe.” And this is so much the case that 
we tend to believe that the meanings of words or other written 
or spoken signs are nothing more than images in the mind, 
either in our own or another mind. Being in the habit of discov- 
ering the significance of most signs via the route of imagery, we 
fail to observe that what is meant by words or other signs is not, 
as a rule, a set of images, but the things for which these images 
stand. If I say, “The sun is shining brightly outside my win- 
dow,” the reader may believe that when he has called up a pic- 
ture of sunlight streaming through a window he has before him 
the meaning of this sentence. But the sentence means neither an 
image in my mind nor in his. It means through these mental 
events to something else. (This does not deny that some words 
and sentences mean images only; ¢.g., “my mental picture of 
China” refers only to ideas in the narrower sense of this term.) 

It cannot be maintained that all meanings terminate in 
images and that when this type of symbol is absent there is no 
meaning. Images as well as other symbols are not confined in 
their significance to any class of objects. They may stand for my 
own or another person’s psychical states, for the content of a 
perception, for other symbols, for objects that have never en- 
tered any one’s experience; and not only may symbols stand for 
any kind of object, they may, as will presently be shown, stand 
for no object and still be significant. 

Some objects are, to be sure, more accessible than others. I 
have a closer knowledge of my own feelings and perceptions 
than of another person’s. The paper on which I write is open to 
inspection in a way that the other side of the moon is not. But 
symbols can refer to the inaccessible as well as the accessible; 
and if there are any objects which symbols cannot mean, these 
will appear only when we have thoroughly examined the ob- 
jects they can mean. 





MEANING 13 


The observation that symbols may mean any kind of object 
frees us from the presupposition that all meanings terminate in 
the present content of the mind, and at the same time leaves 
open the question as to the metaphysical status of the objects 
meant. 


III 


We have said that images pass readily to a second level of 
knowledge, that of significance; and that other objects, spoken 
sounds, written marks, gestures, also take on significance, 
though somewhat less easily than images. 

Below this level of significance (at least of pure significance) 
is a primary level of acquaintance, and all objects which are sig- 
nificant are also objects with which we are acquainted. Whether 
the symbol be a sensation, an image, a perception, whether it be 
believed to belong to the physical or mental world, this symbol 
will be something presented, and will belong to the primary as 
well as the secondary level of knowledge. This immediate way of 
knowing, by direct presentation, is the basic form of knowledge, 
and it has been frequently distinguished from a less direct way 
— knowing of or about objects. I am, for example, presented 
with the groups of letters and words on this page and through 
them I know about the subject under discussion; when I say 
that I know the whiteness of this paper, it is clear that I do not 
use the verb “‘know”’ in the same sense as when I say that I 
know Marcus Aurelius was a Roman Emperor. I am acquainted 
with the one object but not with the other. 

Knowledge about things springs from acquaintance with 
them or with other things in terms of which they can be de- 
scribed; and though it is difficult to explain what it is to be 
known in the sense of being immediately presented to a mind, 
without this sort of knowledge we should probably know 
nothing. We are here in contact with a fundamental concept of 
our theory, the concept of the presentation of objects. 


14 SYMBOLISM AND TRUTH 


Among the objects presented, some take on meaning and be- 
come symbols, while others remain merely presented. What is 
given to the mind becomes an instrument by means of which 
things not given are represented, and thus we begin to pass from 
immediate to purely mediate knowledge. To know about things 
is to refer to them through symbols when they are not presented, 
while to know things immediately is to have them before the 
mind, not simply as something referred to, but as something 
given, in which symbolic references terminate. My knowledge 
that Marcus Aurelius was a Roman Emperor is exhausted by 
statements I can make or ideas I can entertain. I can speak sig- 
nificantly of him, I can think about him, but I cannot be pre- 
sented with him. And this is true of all events in the past and 
future, of distant places, and probably of other minds. I can, at 
the moment, reach these only through symbols. On the other 
hand, my knowledge of the object I call “‘the whiteness of this 
paper” is not exhausted by what I can say or think about it. 
This knowledge is more than a significant idea or statement; it 
is an immediate presentation. 

The most striking fact in knowledge is that it falls into these 
two divisions, mediate and immediate; that mediate knowledge 
is wholly symbolic, a reference to objects through objects, while 
immediate knowledge, even though it may be partially medi- 
ated by symbols, is more than reference to objects. It is a unique 
seizure of objects by the mind. Yet this distinction between 
mediate and immediate knowledge is not so sharply marked 
as many contemporary schools of philosophy, especially those 
which maintain that knowledge is constructed from sense data, 
would have us believe. 


IV 


Objects which are presented are not merely sensed. The unit 
of cognition is not a sensation but something much richer. Sen- 


; 
: 





Ce 


ee ae 


MEANING 15 


sations are discovered as elements in larger wholes, and these 
larger wholes are perceptions or objective presentations. The 
datum of the theory of knowledge is much nearer to William 
James’s stream of thought than to pure sensation. 

“Most books (of psychology), says James, “‘start with sen- 
sations, as the simplest mental facts, and proceed synthetically, 
constructing each higher stage from those below it. But this is 
abandoning the empirical method of investigation. No one ever 
had a simple sensation by itself. Consciousness, from our natal 
day, is of a teeming multiplicity of objects and relations, and 
what we call simple sensations are results of discriminative at- 
tention, pushed often to a very high degree.” ! 

Empiricists rarely mean by “‘experience”’ that which is given 
wholly through the senses at the moment of experiencing. We 
experience objects, relations, qualities; we perceive things of cer- 
tain sorts rather than of no sort in particular; we are presented 
with situations and facts, rather than with bare sense data. 
From this full experience certain irreducible elements that come 
from the senses can be analyzed out; these are elements such as 
white, hard, smooth; but these elements are not the whole of the 
experience. They are always bound up with other elements. 

The cognitive unit, a presentation, is therefore complex. It in- 
cludes a concept (and often a belief) as well as sensations. If I 
gaze from my window at the trees bending in the wind, there is 
much more in my mind than impressions of color, movement, 
shape, and relative position. I see the trees. My mind leaps be- 
yond sensations to concepts — concepts of solid three-dimen- 
sional objects of a certain nature. The fusion of concepts and 
sensations is the presentation of the object, and neither con- 
cepts nor sensations by themselves would give the peculiar kind 
of cognition I call “presentation.” The simplest experience, e.g., 
that of the color white which is now before me, is more than a 


1 W. James, The Principles of Psychology, vol. i, ch. ix, p. 224. 


16 SYMBOLISM AND TRUTH 


pure sensation. I recognize something as white, and in doing so 
bring it under a concept. 

Thomas Reid, the leader of the Scottish school of common- 
sense philosophy, which succeeded Hume, adds that belief also 
is a constituent of perception. We believe “irresistibly,” he says, 
in the existence of the object perceived. But this is not always 
the case. An illusion may be present, actually perceived, but not 
believed; we often doubt our perceptions; seeing is believing 
only to credulous minds. Though there is a strong tendency to 
believe our perceptions, this tendency cannot be a constituent 
of the perception, since perceptions persist when they are 
doubted or disbelieved. A concept, on the other hand, is a neces- 
sary part of a presentation. 

The concepts which enter in perception may function explic- 
itly, as when I judge that “this is white,” or they may function 
silently, without conscious judgment, as when I perceive the 
whiteness. But one knows that he is presented with an object 
only when he brings it, in some way, under a concept. The fact 
that immediate knowledge can deceive, that we are as vividly 
presented with objects in dreams and hallucinations as in other 
states, bears witness to the presence of concepts in immediate 
knowledge. It is only because the stuff of perceptions is largely 
manufactured or elaborated by thought that we can be thus led 
astray. If there were such things as pure sensations, it could be 
readily granted that they would not deceive. They could be 
what they were known to be, and nothing else. But since there 
are no pure sensations, we must admit that any presentation 
can be deceptive. The very perception that something is white or 
hot or hard is subject to error. 

“Sensation, then,” says James, “so long as we take the ana- 
lytic point of view, differs from perception only in the extreme 
simplicity of its object or content. ...A pure sensation is an 


abstraction.” ! 
1 W. James, op. cit., ii, 1 ff. 


— 





MEANING 17 


It is evident that the presence of concepts in perception blurs 
the distinction between mediate and immediate knowledge, and 
especially is this so when we see what a concept is. We shall find 
that a concept is a symbol taken with the mental attitude that 
gives it significance. When we conceive of an object we mean it 
or refer to it, we entertain the idea or symbol of it; and thus the 
mechanism of conception is the mechanism of symbolism. Im- 
mediate knowledge, no less than mediate knowledge, presup- 
poses therefore the functioning of symbols in a mind. 

A mind enters on perception with predispositions or inten- 
tions, which determine to a large extent what is perceived; and 
these predispositions are aroused by symbols — ideas, incipient 
vocal utterances, word imagery — which are at work in the per- 
ception.! The sensory elements also operate as signs. When I 
open my eyes on the room in which I now write, the stimuli 
present to my senses awaken (through sensations) concepts in 
my mind; indeed these sensations themselves play the part of 


1 The psychologists of the Wiirzburg school, in recording their experiments 
on the thought-process, speak of these predispositions as determined by the 
Aufgabe, that is, the problem to be solved in any given case. Something very 
like an Aufgabe is, I believe, present in any mind engaged in perceiving, and 
plays an essential part in determining what is perceived. The following passage 
is quoted from a paper by Dr. C. C. Pratt, entitled “The Present Status of In- 
trospective Technique,” in The Journal of Philosophy, vol. xxi, no. 9, April 24, 
1924: “‘ At the congress for experimental psychology at Giessen in 1904 Kiilpe 
made a brief report on some experiments of his own on abstraction in which 
geometrical symbols, the components of which differed with respect to form, 
color, and arrangement, were used as stimuli. By means of instructions the ob- 
servers were determined now in the direction of form, now of color, and now of 
- arrangement. And it turned out that when an observer was under the Aufgabe 
for color, e.g., he could make at best only a very inadequate report on form 
and arrangement — in some cases he reported that form and arrangement 
were not present to consciousness at all. The implications of such a state of af- 
fairs is far reaching. ... As far as accurate observation and unequivocal report 
are concerned, an observer is adequate only to those aspects of a given experi- 
ence which the determining tendency brings clearly into line with the particu- 
lar Aufgabe of the moment; other aspects of that experience fall at various dis- 
tances outside of the sphere of immediate observation and hence cannot be 
made the objects of scientific description.” See O. Kiilpe, “‘Versuche iiber Ab- 
straktion,” in Bericht ti. den I. Kongress f. exper. Psychol., 1904, pp. 56-69. 


18 SYMBOLISM AND TRUTH 


concepts, that is, of symbols. They arouse unuttered judg- 
ments which are carried by images or fleeting and unspoken 
words. Through the whole process, I am aware in immediate 
presentation, not of the sensations alone, but of the objects I 
thus conceive. I see the desk and the rows of books because 
these are what the passing sensations mean. 

If the presence of concepts in immediate knowledge blurs the 
distinction between the mediately and the immediately known, 
still it does not obliterate it. As we travel up the scale from pres- 
entation to representation, we come finally to a kind of knowl- 
edge in which the object conceived or meant is no longer given 
along with the symbols through which it is conceived. This is the 
kind of knowledge embodied in a mathematical expression or a 
scientific theory; or, more simply still, in a judgment as to the 
past or future. It is purely symbolic. Between presentation and 
representation there is a twilight zone in which oné cannot be 
sure whether the object intended is given or merely conceived. 
Here most of the errors of perception occur. But the ends of the 
scale are distinct. At the one end is a direct acquaintance with 
objects such as is not possible through concepts (or symbols) 
alone: this is a cognition in which what is meant is grasped in a 
union of sensation and conception, often attended by belief. At 
the other end is pure conception, knowledge which is significant 
reference and nothing more. 


Vi 


The statement that concepts (symbols) are always to be ) 


found in immediate knowledge must be modified if there is any 
such cognition as M. Henri Bergson’s intuition of the flux of 
reality. The Bergsonian intuition is a pure awareness more im- 
mediate than the perception we have described; it does not give 
presentational knowledge in our sense of the term; it is not an 
acquaintance with objects, not even with simple qualities. 





— 


{ 
‘| 
| 


MEANING 19 


One cannot adequately explain what this intuition gives him. 
He must search for it in his experience and if he finds it must 
admit his inability to express it. He will be unable to bring it un- 
der any concept, but must remain content to gesticulate in its 
direction with words and metaphors. I cannot, in Bergson’s 
sense, have an intuition of an object, for this would require the 
concept of an object — the content of the intuition would be con- 
ceptualized in this general and vague way as “something-or- 
other.”’ Thus if we grant the existence of such a non-conceptual 
form of cognition, it will give us neither objects, qualities, rela- 
tions, things, or events, but will fall into a category of its own, 
beyond all rational categories. 

Now there does seem to be a background of pure awareness 
not unlike the Bergsonian intuition in all presentations. Beyond 
the objects which are clearly given, beyond what is singled out 
and conceptualized as “‘experience,”’ there is something which 
cannot be singled out and conceptualized. This is an amorphous 
datum which transforms itself, under the working of concepts, 
into the articulated data of perception. 

Perceptual knowledge, the knowledge of objects, persons, 
events, places, relations, qualities, sense data, has a structure. 
Only after we have examined this structure will the distinction 
between pure awareness and rational presentation become 
clear. Pure awareness must be the complete antithesis of con- 
ceptual knowledge; it must be knowledge in which all symbols 
have been transcended, knowledge wholly deconceptualized; 
and yet it must be continuous with perception, and through per- 
ception, with conception. The presentation of objects must arise 
from this pure awareness and return to it with no perceptible 
break. 

Theories of knowledge which find pure immediacy in sense 
data do not carry their analysis far enough. The sense datum is 
something discrete, fixed and referred to by a concept, and be- 


20 SYMBOLISM AND TRUTH 


hind the sense datum is the vaguely apprehended whole from 
which it is discriminated. Even so fluid a datum as Mr. A. N. 
Whitehead’s event ! is not known in pure immediacy; the event 
is picked out from a background, and certainly the perception 
of relations between events demands more than a purely im- 
mediate knowledge. 

The attempt to discover the purely immediate leads thus be- 
yond perception and sensation to what can be described only as 
the unarticulated awareness of a whole. (And even this descrip- 
tion is faulty since it makes use of concepts.) But this pure 
awareness is not a form of knowing which can stand on its own 
feet. It issues from the whole cognitive act as the final aroma 
of knowledge, as a sense of oneness with the object known; and 
the attempt to isolate pure awareness meets with no better suc- 
cess than the attempt to grasp a pure sensation. Though this 
intuition passes beyond what can be clearly compressed into 
concepts, it does not contradict but supplements conceptual 
knowledge. We must leave till later the discussion of this pure 
awareness and its relations to other forms of knowledge.? 


VI 


From the basic units of presentational knowledge, purely 
symbolic or conceptual knowledge is constructed. Through sym- 
bols, themselves presented and significantly linked to objects 
(and sometimes to no object), we move from the realm of pres- 
entations to that of representations. It is here that the sciences 
appear, that logic enters, that the common knowledge of every- 
day speech comes into being. The world of the purely concep- 
tual is superimposed on or abstracted from the world of the im- 
mediately known. The mind reaches out from its data. Words, 
ideas, and other signs carry it beyond things that are given to 


1 A, N. Whitehead, The Principles of Natural Knowledge (1919), ch. vi. 
2 See below, ch. VIII, sec. xii. 





MEANING 21 


the imaginary and even to the non-existent, the fantastic, and 
the impossible. And this brings us to the central problem of the 
present chapter, the nature of meaning. 

A symbol, briefly described, is an object which stands for an- 
other object or is still significant if it stands for no object. This 
is no definition, and serves merely to raise the question of how a 
symbol is related to the thing it means and how it can be signifi- 
cant when it means no existing object. 

In the first place, the symbol stands in a mind for an object; 
it takes on significance through psychical activity, and if there 
were no minds there would be no symbols. Since the symbolic 
relation is not something given in the external world, any signifi- 
cance discovered in the events about us is read into these events; 
and quite apart from the metaphysical question as to whether 
these events could be if there were no minds, they certainly 
could not be significant unless they were so interpreted. When 
one says that clouds mean rain, that a low temperature means 
ice and snow, he refers to a causal connection between these 
things, but this relation alone does not make the one a sign of 
the other. It is because the cause is interpreted as a symbol that 
the antecedent event takes on significance. Aside from the con- 
nections of meaning established in a mind, things in the order of 
nature simply are; they are bound together by laws, but not 
bound so that any one by its own nature means any other. 
Berkeley, who interpreted all sense impressions as signs, found 
it necessary to postulate a Divine Mind communicating with 
man through this language of natural events. 

Written marks and spoken sounds are not different in this 
respect from other objects: without a mind which uses them to 
refer to things, they would be nothing more than physical occur- 
rences; and the same is true of images or ideas—unless we took 
them to be significant, they would pass through the mind as 
psychical events, conforming to the laws of association but bear- 
ing no meanings with them. 


22 SYMBOLISM AND TRUTH 


Meaning then is something superadded to things by a mind. 
What is the nature of this activity which adds significance? 

The commonest answer to this question, familiar especially in 
English philosophy from Hobbes onward, is that the meaning 
activity is the association of ideas; and this reappears in James, 
who says that the meaning of an idea is to be found in its “‘psy- 
chical fringe.”’ Locke sees the weakness of this view when he 
speaks of association as a distemper of the mind which leads 
thought away from its objects rather than toward them. In de- 
termining the meaning of a word or image, we must rule out ir- 
relevant associations; much of the “‘psychical fringe”’ must be 
overlooked; and this being the case, meaning must be something 
other than association. Though associations sometimes conduct 
one to the things he means, they more often conduct him away 
from them, and he can never be sure that the paths of associa- 
tion are not by-ways rather than high-roads of thought. The 
associations that play a part in carrying meanings are con- 
trolled, that is to say, their direction is prescribed by what the 
psychologists know as a “determining tendency ”’ or an Aufgabe. 
The word ‘New York” may arouse by association the image of 
the Statue of Liberty, which may lead to a picture of the guil- 
lotine and the red flag, but none of these associated ideas is the 
meaning of ““New York”’; they must be dismissed as irrelevant 
associations. Images of canyon-like streets and suspended 
bridges bring the meaning nearer, since they fit the attitude or 
set of mind the word induces. 

There is a still more damaging objection to the view that 
meaning is the association of ideas. Association is a link between 
images and carries the mind no further than ideas in the nar- 
rower sense of the term; and yet what is meant by a symbol need 
not be an idea. ““New York” means the city on the banks of the 
Hudson, rather than the representation of this city in images, 
and these images themselves mean something other than images. 





MEANING 23 


They stand for a perceptual object, and the word means what 
the images mean. The activity of meaning is, more frequently 
than not, directed beyond ideas, and so it cannot be described in 
terms of association, which is restricted to ideas. 


VII 


The simplest solution for the purposes of the theory of knowl- 
edge is to accept as unique a meaning activity. This does not im- 
ply that from the point of view of psychology this activity is 
unanalyzable; it may well be that it can be reduced to more ele- 
mentary activities, but it is not necessary for our present 
purposes to do so. We must confine ourselves to a general 
description, which is intended to direct the reader to the point in 
experience where the meaning activity is to be found. Having 
discovered meaning in its primitive form, we can show how 
more complex meanings are constructed, and this will lead to the 
logical and strictly epistemological, rather than psychological, 
aspects of the subject. 

To reach out with the mind toward objects, as one does when 
_ he means them, is to be in a state of preparation for these ob- 
jects. The meaning activity is one of vague anticipation: the 
mind is poised expectantly, awaiting something other than the 
thing, the symbol, which is immediately before it; and this an- 
ticipation is vague because it is not accompanied by a belief that 
the object meant will appear or that it exists. When I mean an 
object I do, in some sense, prepare my mind for a presentation 
of this object. Though I cannot be said to turn my attention 
toward the thing I mean, since one cannot attend to something 
not presented to him, there is no doubt that I do more than at- 
tend to a symbol or an image. Indeed, I turn my attention away 
from the symbol or the image, and this constitutes the first step 
in preparation for the thing meant. 

Toward every object certain activities are appropriate. I can 


24 SYMBOLISM AND TRUTH 


eat bread; I can throw a stone; I can sit on a chair. These 
activities are appropriate to the object for many reasons, the 
most important of which are biological reasons: the appropriate 
activities are those which enable me to adapt myself to the 
thing; and for any single thing there are many such activities. 
When a symbol is before the mind, it sets in motion the activ- 
ities appropriate to an object and this object is then what the 
symbol means; but it sets these activities in motion only par- 
tially, it touches nothing more than their psychical roots, so 
that if the effect of the symbol appears in consciousness, it is as 
a barely noticeable feeling of tendency. 

Physiologically, a symbol probably stirs the central part of a 
chain of nervous connections which constitute a tendency to act 
in a certain way. The process of understanding a symbol ter- 
minates in the brain, and for this reason the activities it arouses 
are implicit, so implicit as to diminish almost to the zero-point 
both for outward and inward observation. And yet they are ade- 
quate to carry the reference, the outward reach of the mind, 
which is significance. 

Ideas, as well as written and spoken words, set up these cen- 
tral tendencies to action. Every idea, in James’s opinion, has its 
motor side; and not only do ideas arouse tendencies to action, 
they spring from these tendencies, so that the set of the mind in 
a certain direction determines what images appear and causes 
irrelevant images to be disregarded. It is this set rather than the 
image itself which fixes the meaning, and this is why ideas do 
not mean by resemblance alone. 

But what if the activities brought into play by a symbol be- 
come overt? What if they push out beyond the central nervous 
system and terminate in completed acts? 

In this case the mind has gone further than merely under- 
standing the symbol. Understanding has passed into belief, that 
is, one has begun to behave as if the thing meant were present, 





MEANING 25 


as if the activity which is fitted to it could be successfully per- 
formed here and now. Understanding and belief being of the 
same genus, the line which separates them cannot be sharply 
drawn. Belief is willingness to act on what is understood, while 
understanding is preparation for activities appropriate to an ob- 
ject, though these activities are checked far short of perform- 
ance. 

If you tell me that it is a good day for a walk in the hills, I 
understand by putting myself in an attitude of mind suited to a 
walk in the hills, but this attitude does not amount to belief. 
Though I need not actually set out on the expedition if I believe 
the statement, I must nevertheless be more fully prepared to do 
so than if I merely understand it. I must feel that the walk could 
be successfully undertaken. Belief is a more complete prepara- 
tion for activity than understanding: it is understanding with an 
added psychical pressure in the direction of performance. There- 
fore, if the effect of a symbol on a mind is to produce overt acts, 
we can conclude that the symbol is not only understood but also 
believed. 


VIII 


This is not the only possible conclusion, and here the inade- 
quacy of the behavioristic treatment of meaning comes into 
view. 

The extreme behaviorist assumes that there is only one way in 
which psychical processes can be studied, namely through out- 
ward action. Now an object that is immediately presented may 
produce outward activity without either understanding or be- 
lief. Certainly if one is to believe, he must begin by understand- 
ing, for he cannot believe what he does not understand even in a 
vague sense; and so if overt activity does not testify to under- 
standing, it cannot prove the presence of belief. The crucial 
question in the behavioristic account of thought is, then, does 
overt activity indicate understanding? 


26 SYMBOLISM AND TRUTH 


Let us suppose that our dog comes for his food when the 

dinner-bell is rung. The bell has aroused an activity appropriate 
to an object, and we can assume that the bell means dinner to 
the dog; and yet we cannot be sure of this. The dog’s act is not 
different, so far as we can know, from many other habitual acts. 
He will go to a certain corner each night to sleep, he will bark at 
certain persons and not at others, he will howl when the moon 
is full. Are we to say that all of these acts are acts of under- 
standing? . 
_ The weakness of the behavioristic theory of meaning is that it 
affords no criterion by which acts of understanding can be dis- 
tinguished from other habitual acts, yet no one would be willing 
to say that all such acts are cases of understanding. The theory 
leads us to the conclusion that any stimulus to which we react in 
an habitual way is a symbol. 

It is true that most signs acquire significance through habit. 
The connection between the sign and its meaning is based on a 
conditioned reflex. The object A, food, for example, stirs the 
activity B, hunger and eating; and if X, the sound of the dinner- 
bell, accompanies A for a sufficient number of times, X alone 
will become an adequate stimulus for these activities. This is the 
pattern of all habits. But there is a distinction between habits 
which carry meaning and those which do not. Though we should 
have no speech and writing were it not for our ability to form 
habits, the formation of a habit does not argue a connection of 
meaning; there are many habits in our behavior that are not 
vehicles of significance. 

Habits of meaning belong to a special class. They are abbrevi- 
ated habits, habits purely of the mind, not extending beyond the 
central nervous system. When we understand a word or an idea, 
we perform no observable acts, unless it be silently to repeat the 
word. The actions appropriate to the object are confined to the 
brain, or nearly so; and it is just this mental or inner character 


MEANING Q7 


of habits of meaning which differentiates them from meaning- 
less habits. A sign causes us to think rather than to go off into a 
series of immediate and unreflective acts, as do other habit- 
stimuli. Deliberation, abbreviated action, understanding, rather 
than overt activity, are the effects produced by symbols. 

The behaviorists explain that meaning is based on language 
habits and that meaningless vocal acts or habits develop into 
language habits, which carry significance when they become 
associated with “arm, hand, and leg activities and substitutable 
for them.” ! This is an attempt to formulate a criterion of signifi- 
cant as opposed to meaningless habits. The substitution of a sign 
for an object indicates that the sign is understood, that is, that 
it has become a sign. But substituted how? Substituted where? 
And here the whole problem of meaning is concealed. The only 
intelligible answer is, substituted in an internal experience not 
open to external observation. 

It is impossible without introspection to say when this substi- 
tution has taken place. Mr. J. B. Watson’s example of such a 
substitution is inconclusive: the fact that sounds are uttered in 
conjunction with arm, hand, and leg activities,— in conjunction 
with an infant’s reaching for an object held out toward him,— 
and that the sounds alone are uttered at a later time, either 
when the object appears or when it is absent, does not show that 
the sound has been substituted for these activities, that the 
child has passed from unreflective action to deliberation, and 
that the sound has come to mean the object. The substitution of 
a symbol for an object, which is its “‘standing for the object,” is 
essentially a fact for introspective observation and only secon- 
darily a fact of behavior. 

Meaning is an activity that can be described only in intro- 
spective terms, and even in introspection it is difficult to grasp. 


1 J. B. Watson, Psychology from the Standpoint of a Behaviorist (1919), 
pp. 319 ff. 


28 SYMBOLISM AND TRUTH 


Thought is distinguished from action simply on the ground that 
it is activity which does not work itself out in behavior. If 
thought is behavior, it is behavior inhibited and yet fully aware 
of its directions and intentions. The habits on which it is built 
are private. Though it may be true that the dog genuinely thinks 
dinner at the sound of the bell, we are not justified in inferring 
that he does from his behavior alone; and if our own reactions to 
dinner-bells and to words or images were always overt and fully 
carried out, if we could not pause to deliberate and so check, 
short of performance, the tendencies to action aroused by sym- 
bols, we could not be said to understand language or ideas, but 
only to react to them as we might to a bright light or a loud 
noise. The moment of suspension of mind between the immedi- 
ate stimulus and the activities that follow would be shortened to 
exclude understanding, and none of the stimuli of habitual ac- 
tions would become symbols. They would remain merely ob- 
jects which set in motion conditioned reflexes, and their capacity 
to mean other objects would be as yet unrealized. 

No doubt there is an insensible gradation between habits that 
do not carry meaning and habits that do, and by this gradation 
an organism passes from action to thought. As the capacity to 
retain the effect of a stimulus in the mind without overt activity 
increases, the ability to understand is gained, and the objects to 
which the organism has before reacted habitually without un- 
derstanding become symbols of the things toward which these 
activities are directed. Unless this capacity to suspend reactions 
and to anticipate an object rather than to behave as if it were 
present were developed, we should not be able to think but only 
to act. 


IX 


The psychological aspects of meaning can be summarized as 
follows. A significant reference to an object with an object is ac- 
complished through a suspension of activity, known in intro- 


MEANING 29 


spection as an intention. A symbol touches a train of psychical 
connections which, if followed out, lead to activities appropriate 
to an object. In understanding alone, this train of connections 
is remotely stirred and is not pushed to its terminal point, but 
when the suspension of mind breaks over into the actions suited 
to the object, understanding passes into belief. Belief must be 
preceded by understanding, and overt activity is not necessarily 
a sign of belief or of understanding. In this suspension of activ- 
ity the mind reaches out beyond its immediate field, and the 
stimulus of this outward reach, whether it be an image, a word, 
a mark, or a gesture, is a symbol. 

A general conception of what it is to think can now be framed. 
Without symbols there is no thought. Thinking is activity, or 
rather the suspension of activity, through symbols. It is the sub- 
stitution of symbols, which are in the field of presentation, for 
the things intended by the symbols, which may be beyond this 
field; and sometimes thought is carried by symbols that stand 
for no objects. Thought is not to be classified with sensations, 
images, feelings, conations, as an element of consciousness. It is 
built up from these elements, and it may be from others; it is the 
use of these elements for the purpose of recording and conveying 
significant references. 

If psychologists have discovered an imageless thought, they 
have not discovered a thought which does not rest on the use of 
symbols. Symbols are the universal instruments of knowledge, 
and the ancient logicians who defined man as a “rational ani- 
mal” might well have given another definition, ‘employer of 
signs,” for man’s rationality consists in his ability to use signs. 
Without the semi-artificial media of language, writing, and the 
numerical system, human knowledge as we know it could not 
have come into existence; and beneath these systems of semi- 
artificial signs lies a still more primitive system, that of images. 

To indulge in pure thought is to put in the place of the things 


30 SYMBOLISM AND TRUTH 


found in experience a set of substitutes, secondary realities such 
as marks on a page, vocal noises, psychological images, and to 
move in this world in a way corresponding to that in which one 
might have moved among the primary realities. And thought is 
more than this: it is the extension of the references of symbols 
beyond the experienced, it is the significant use of signs when 
there are neither presented nor existent objects for which they 
stand. These more complex types of meaning remain to be con- 
sidered. 


xX 


It is not difficult to see how things such as colors, shapes, 
sounds, simple states of mind — anger, fear, pleasure, pain — 
can be referred to; but one speaks significantly also of “‘the uni- 
verse,” “‘the world,” “the solar system,” and yet none of these 
objects has entered experience in its wholeness, nor is there any 
single activity or set of activities appropriate to it. This is true 
also of more restricted objects such as ““New York City” or 
“the British Empire.”’ We cannot mean these things merely by 
taking a single symbol to stand for them. The mind must reach 
out toward them in some immensely more complex fashion than 
it does toward simpler objects. 

All of our most complex ideas, says Locke, even to the idea of 
God, are constructed from simpler ideas which are the founda- 
tions of knowledge; and Locke’s distinction between simple and 
complex ideas can be extended to all symbols. Objects such as 
the universe, the other side of the moon, the continent of Europe, 
are referred to by means of complexes of references to simpler 
objects. 

Most of the things with which we are familiar are easily seen 
to be composed of other things, they can be separated into ele- 
ments; and if an object as a whole cannot enter experience to be- 
come the terminus of a meaning, some or all of its components 
usually can. Though we cannot directly form habits of speech or 


MEANING 31 


thought appropriate to the universe or to New York City, we 
can come in direct contact with parts or aspects of these objects. 
These objects can be analyzed and thus can be represented in 
thought; the whole can be grasped through its elements. 

The symbolic systems of language, mathematics, and the 
imagination are peculiarly adapted to this analytical representa- 
tion of objects. Men think not by means of isolated words, signs 
or ideas, but by joining these into groups, into propositions, 
phrases, and sentences, which have a meaning as a whole. This 
is syntactical meaning. Syntax is literally “taking together,” and 
symbols taken together are significant, as symbols by themselves 
cannot be: any phrase, sentence, or complex idea — any group 
of symbols — has a meaning other than the meanings of its ele- 
ments but determined by these, and these alone. This gives us 
the first principle of symbolism, the principle of syntactical sig- 
nificance: the significance of any group of symbols is a function of 
the significance of its members. To the elements of a symbolic 
group correspond elements of the object which might be meant 
by the group as a whole, and thus, through a symbol that can be 
analyzed into parts, an object that can be likewise analyzed is 
represented. The sentence, “‘the sun is shining outside my win- 
dow,” means a fact composed of the objects meant by “‘sun,”’ 


99 66 99 66 


“shining,” “outside,” “my,” and “‘window.”’ The fact is these 
elements, built up according to a definite plan, taken in a certain 
order, and the meaning of the sentence is a synthesis of separate 


meanings in a single meaning. 


XI 


Before we can employ groups of symbols to represent objects 
analytically, we must be equipped with simpler instruments of 
thought. These are simple symbols, whose significance is of the 
direct sort described above. 

Simple symbols have no syntactical meaning. Their signifi- 


32 SYMBOLISM AND TRUTH 


cance is not a function of that of their parts, if they have sym- 
bolic parts, but rather a function of the presentation of objects 
and of a mind which establishes connections of meaning between 
presented objects. The significance of “Shakespeare”’ is not de- 
termined by the meanings of “shake” and “‘speare”’: it arises 
from the direct use of this name for a person. (A simple symbol 
may have meaning, however, through definition only, that is, it 
may be defined as equivalent to a symbolic group, e.g., “nectar” 
is “the food of the gods”’; and in this case the meaning will not 
be a function of the presentation of an object for which the sym- 
bol is taken to stand.) The conditions under which simple sym- 
bols acquire meaning are such that they cannot mean objects 
which have not appeared in perception, unless they are expressly 
defined through symbolic groups which mean such objects. 
Knowledge is built on experience, on presentation, because it is 
only in experience that these first instruments of knowledge are 
of use. In order that (undefined) simple symbols may take on 
meaning for us, we must have performed acts directed toward 
the things they mean. We must have experienced the symbol 
with the object, and a conditioned reflex must have been estab- 
lished, so that when the symbol appears the appropriate activ- 
ities and the intention directed toward the object will be set up. 

It was said above that without concepts, that is, significant 
symbols, there are no presentations of objects, and it should be 
added that without presentations of objects there are no con- 
cepts. Simple symbols, that is, single words or ideas and the 
psychical attitudes which accompany them, play a necessary 
part in determining the cognitions of their objects, and at the 
same time the cognitions of these objects play a necessary part 
in determining the meanings of the simple symbols: they are 
functions of one another, and it is impossible to say that the 
presentation of objects precedes in time the use of symbols. 
Perception is born through the significant use of symbols, and 
the significant use of symbols, through perception. 


a i 


MEANING 33 


The significance of a simple symbol, unless it is defined 
through a symbolic group, rests on three necessary factors: first, 
the symbolic object proper, the mark, the image, the sound; 
then the attitude of preparation, the intention or psychical set; 
and finally the presentation of the object meant. To say that a 
concept enters in every perception of an object means simply 
that these three factors are always present in perception. I am 
never presented with a thing unless I am also presented with a 
sign appropriate to the thing. Significance of this simplest sort 
is a part of every experience. Symbols and the mental attitudes 
which accompany them pick out things, relations, qualities, 
sense data, from the background of pure awareness and make 
them objects of knowledge. Signs are a genuine part of presenta- 
tions, and we come originally to know their meanings apart from 
presentations by separating them out, rather than by artificially 
creating and applying them. The artificially created sign is a late 
product in the evolution of thought. Having been sifted out 
from the presentation of which it was in the beginning a part, 
the sign can mean when the object meant is not presented, but 
it could not mean this object unless the latter had been pre- 
sented. 

It is less evident that words are integral parts of presenta- 
tions than that images are. Words probably appear later than 
images as carriers of cognitive attitudes. But theories of the de- 
velopment of language assume that words were originally bound 
up with perceptions. Those who believe that language arose, in 
part at least, from ejaculations say that a noun such as “‘ache”’ 
comes from the ejaculation “‘ach!”’ the cry of pain; the pronoun 


+>? 


“me” from the ejaculation “ahem!” by which the speaker in- 
voluntarily calls attention to his own presence.! Cries and vocal 
expressions, once parts of an experience, were thus cut off from 
the whole and became significant in their own right. Certainly 


1G. Willis, The Philosophy of Speech (1920), p. 9. 


34 SYMBOLISM AND TRUTH 


in our adult perceptions we are often conscious of the passage of 
words through the mind as a means by which we adjust our- 
selves to the object perceived. 

There can be little doubt that all perceptions include a psychi- 
cal set toward the object. The mind is not purely passive in per- 
ception, as Locke supposed — not a tabula rasa on which experi- 
ence writes. Perception is an activity, and mental activity is 
always directed toward something; it always intends something. 
This active attitude of intending, which is the second essential 
of simple meaning, is more prominent in perception than the 
first, that is, the symbol proper, to which this attitude is at- 
tached. But the first is nevertheless present. The symbol proper 
arises somewhere in the course of the perception, and the three 
elements, symbol, attitude, and object, are united in a whole 
which is the presentation of the object. 

Thus, as far back as we can trace our articulated experience, 
simple concepts are present in it, and these have meaning only 
through experience because they are of the very stuff of experi- 
ence. 

These elementary symbols (concepts) stand for data. When a 
single word, gesture, or sound has once been taken as significant 
without definition, a datum has been accepted; and though sub- 
sequent use of the symbol may lead one to observe that the ob- 
ject it refers to is complex and can be analyzed into new data 
signified by other symbols, still no analysis can be pushed so far 
that all data disappear. But it must not be forgotten that many 
simple symbols have meaning only through definition. “Santa 
Claus”? means the same as “the good saint who fills up our 


b 


stockings at Christmas”; “the universe” is a name for “the 


totality of objects, known and unknown”’; “matter” a name for 
“objects that obey physical laws.” Such defined symbols are 
abbreviated forms of more complex meanings. They are derived 


concepts whose objects are not data. 


MEANING 35 


XIT 


Having once at our command a stock of the simpler instru- 
ments of meaning given in our commerce with the immediate 
environment, we can construct new meanings determined by the 
old. Through these the imagination takes wings and the world 
of speculation is opened. 

A symbolic group, if it stands for anything, will stand for a 
complex object, which may be the kind of object signified by a 
descriptive phrase such as “‘the center of gravity of the solar 
system,” or the kind signified by a completed sentence either 
asserted or unasserted, e.g., “knowledge is power.” The latter 
type of symbolic group is ordinarily termed a proposition. The 
peculiarity of a descriptive phrase is that through a complex of 
predicates or relations it signifies a term, while the meaning of a 
proposition, on the other hand, is not focussed on a single term.! 

The constituents of the complex object meant by a symbolic 
group are signified by simple symbols, and it is clear that these 
constituents must have been given in experience or must be de- 
finable through symbolic groups whose simple symbols refer to 
elements given in experience. ““New York” means “the city at 
the mouth of the Hudson,” and if the objects meant by “‘city,”’ 
“at,” “‘mouth,” “of,” and “Hudson” cannot be known di- 
rectly, they must be defined in terms of objects that can be 
known directly; that is to say, every symbol (simple or complex) 
must signify a datum or be reducible to symbols which signify 
data. And yet a descriptive phrase or proposition whose simple 
symbols refer to data or are defined in terms of references to 
data, may as a whole stand for no object; it may state no fact, 
describe nothing, and still be significant. Thus the phrase, “the 
hereditary monarchs of the United States,”’ has meaning though 
it describes no one; the proposition, “‘the gods live on nectar and 
ambrosia,” states no fact, yet it is significant. 


1 See below, ch. IV, for a discussion of this distinction. 


36 SYMBOLISM AND TRUTH 


Both reason and imagination rest on this possibility of using 
symbols significantly when there is nothing to which they refer 
— a possibility which arises through joining simple symbols into 
groups. The meaning of the group is a function of nothing but 
its subordinate meanings and — what is more important still — 
of its logical form. No object meant need be presented; the 
being, either in or out of experience, of an object to which the 
group as a whole refers is irrelevant to the meaning, for group- 
meanings are determined by meanings alone. 

Many writers dismiss the possibility of thinking or speaking 
significantly when there is no object thought or spoken of, by a 
simple argument. To think when there is nothing thought of is 
not to think; to mean when there is no object meant is not to 
mean.! It is denied that symbols can be used significantly when 
they do not refer to existing objects. This is indeed true of unde- 
fined simple symbols but it is not true of symbolic groups. The 
argument rests on the assumption that all meaning is simple 
reference to an object with an object, and the more subtle type 
of reference through groups is neglected. 

Syntactical or group-meaning is, like all meaning, an outward 
reach of the mind, but it takes an indirect course and may never 
terminate in an object. A phrase sets up all the anticipations or 
intentions its single words arouse; when I understand the signifi- 
cance of “‘a sunny day in spring,” I am stirred psychologically 
as I would be by “‘sunny,” “day,” and “spring”; I take an atti- 
tude appropriate to the things meant by each of these words; 


1 Plato puts this argument in The Sophist, Jowett’s translation, marginal 
page 237: 

Stranger. You mean by assenting to imply that he who says something 
must say some one thing? 

Theaetetus. Yes. 

Stranger. Then he who says “not something”? must absolutely say 
nothing. 

Theaetetus. Most assuredly. 

Stranger. And he who says “‘nothing,”’ is not to be described as speaking; 
and therefore he who says “‘not-being”’ does not speak at all. 


MEANING 37 


but my attitude is at the same time a unity. I anticipate these 
elements as forming a whole, and if no such whole exists the atti- 
tude of mind will still carry the meaning. Through the many 
references of its members (and its logical form) the symbolic 
group, as a unity, has a reference, that is, a direction toward 
something; and even though there is (or has been) in experience 
no object for which the expression as a whole stands, there will 
nevertheless be a locus in experience toward which this unitary 
reference is directed. This is the locus of the objects meant by 
the elements of the group. There is no “present king of France”’; 
and yet this phrase tells me where to seek for the object it 
might mean. A symbolic group means through a complex inten- 
tion constructed from simpler intentions, and so performs the 
function of referring, which is the essence of meaning, when as a 
whole it refers to nothing. 

Syntactical meaning — a meaning of the whole determined 
solely by that of the parts and their plan of unity — can be 
found in any phrase, sentence, mathematical expression; in 
short, in any group of symbols. Its requisites are: (1) a number 
of simple symbols referring directly to objects, or defined in 
terms of such references, and (2) a unity of these symbols and 
the intentions which attach to them in a single intention. It is 
not necessary that this complex intention should arise from or 
terminate in any single object. 

The manner in which the simple symbols are joined into a 
unity gives the expression a structure, and it is in the analysis of 
this structure that the central problems of the theory of knowl- 
edge appear. It may seem to the reader that the structure of 
symbolic groups is merely a matter of grammar. What possible 
light can the study of grammatical forms throw on knowledge? 
The fact is that grammatical forms are reflections of logical 
forms; and if the study of the structure of symbolic expressions 
is grammar, it is what has been called “philosophical grammar” 


38 SYMBOLISM AND TRUTH 


—an analysis of the structure of thought. In order to under- 
stand what is meant by the form of a symbolic complex, it is 
necessary to probe deep into the nature of knowledge and its 
objects. But before we turn to this topic, let us put together the 
facts of knowledge which are now before us. 


XIII 


The objects of knowledge are not ideas, unless “idea” be 
taken in the broad sense of any known object. Ideas in the sense 
of “images”’ can be distinguished from sensory and perceptual 
objects, and the objects of knowledge may be either images or 
sensations and perceptions. Ideas in the narrower sense occupy 
a special place in thought: they are the most primitive type of 
symbols, the primary carriers of meaning. Ideas need not signify 
merely the sensory or perceptual objects they resemble: any 
idea may mean any thing. Moreover, semi-artificial signs such 
as those of speech and writing supplement images, and in some 
cases completely supplant them. It is important to observe that 
no symbols are restricted to meaning a particular class of ob- 
jects, least of all to meaning ideas in the narrower sense. 

The study of the principles of symbolism, which is also the 
study of the mechanism of conception (for a concept is nothing 
more nor less than a significant symbol), provides a single point 
of view from which to approach knowledge. 

Knowledge as a whole falls into two great divisions: mediate 
and immediate, knowledge about and acquaintance with objects. 
The former rests on symbols alone; the latter is a union of sym- 
bolic knowledge and direct apprehension. The presentation of 
objects, that is, experience, is always attended by the functioning 
of symbols (of concepts) in the mind, and intending or meaning 
an object is a part of every experience. The mind is not a tabula 
rasa but an active agent in perception, and so the line between 
mediate and immediate knowledge cannot be sharply drawn. 


MEANING 39 


But immediate knowledge is not sensation, for sensations do not 
appear by themselves but only as elements in larger cognitive 
units, in which they usually play the part of signs. All so-called 
“immediate” knowledge is partly mediated by concepts, with 
the exception of pure awareness, which is the complete antithesis 
of conceptual knowledge and the only form of pure immediacy. 
Pure awareness is not the cognition of objects, relations, qual- 
ities, or sense data: it is the apprehension of an unarticulated 
datum. Pure awareness cannot be dissociated from the act of 
knowledge as a whole. 

Signs have meaning only through the activity of minds. Nat- 
ural objects, even images, are not significant unless they are 
taken to be so by a mind. The meaning activity is a preparation 
for the object meant, but a preparation which goes no further 
than the central nervous system, and which appears in con- 
sciousness as an intention. Belief, which is of the same genus as 
understanding, is a completer preparation for an object: it is 
willingness to act as if the object were in existence. Understand- 
ing arises only when the mind is able to suspend the activities 
appropriate to a thing, and to deliberate rather than act; and 
though meaning rests on habit, it is not the association of ideas, 
nor is it the type of habitual response which leads at once to 
outward action. Thus it is impossible to describe meaning wholly 
in terms of behavior. 

There are two types of meaning, one of which is built on the 
other: (1) simple and (2) syntactical meaning. Simple symbols 
are objects taken by a mind to stand for other objects: their sig- 
nificance is not a function of their parts and, unless their mean- 
ing is defined, they have meaning only through direct reference 
to things which are (or have been) experienced. The significance 
of these undefined simple symbols rests on direct experience be- 
cause they are an integral part of the presentation of the object 
to which they refer. 


40 SYMBOLISM AND TRUTH 


Complex or syntactical meanings (so called because they are 
created by taking together simple meanings) are functions of 


other meanings; and this sort of significance, which attaches to 


any phrase, sentence, or mathematical expression, rests on the 
general principle of symbolism, that the meaning of a symbolic 
group as a whole is determined by the meanings of its elements. 
A symbolic group represents an object analytically, that is, as a 
unity of elements with a form; but a symbolic expression may be 
significant when it stands for no object, for its meaning is a func- 
tion of meanings only and not, as in the case of an undefined 
simple symbol, of the presentation of an object. 

Now that we have a general notion of what meaning is we can 
enter on a wider problem — that of showing how the structure 
of symbolic expressions points beyond itself to the structure of 
the world of fact. The garments in which knowledge is clothed, 
loose and ill-cut as they often appear, reveal the outlines of the 
form beneath them; syntax and grammar, which seem to be 
conventions of human intercourse, spring from the adaptation 
of the mind to an order which pervades its environment. 


CHAPTER II 


LOGICAL FORM 


I 


Menrsztx to place a number of symbols together at random 
does not make them a symbolic group. The phrases of language 
are not chance combinations of words; they have a structure, 
and certain word-structures are significant while others are not. 
The same words in one combination mean one thing, and in an- 
other combination, another thing. The problem of the structure 
of significant phrases cannot be solved by showing that any 
group of words which conforms to the rules of syntax in lan- 
guage is significant, for this leaves the rules of syntax to be ex- 
plained. 

Every symbolic system, whether it be speech, mathematics, 
logic, or the system of mental images, has its own rules of syn- 
tax. Within the system some combinations of symbols are signif- 
icant and others are nonsensical. Some of these principles are 
arbitrary: they have grown up through usage, as have the mean- 
ings of the individual signs, and usage can alter them; but they 
are not all arbitrary. The structure of every symbolic system is 
the same in general outline; it is modeled on the structure of 
fact, for every symbolic system, if it represents anything, will 
represent facts. 

The meaning of a symbolic group is, for this reason, not 
purely a matter of choice, as is the meaning of a simple symbol. 
There are certain objects that the group can signify, and other 
objects that it cannot signify. The structure of the group fur- 
nishes a criterion which enables us to determine its possible 
meanings. At first sight it might seem that groups of symbols 


42 SYMBOLISM AND TRUTH 


could represent anything, as can simple symbols. Simple sym- 
bols are attached to their objects only accidentally, through 
habit or definition. We can change our conventions for their use 
as we please. Why is this not also true of symbolic groups? Are 
not all symbols arbitrary and accidental in their meaning? 

If this were so, the problem of how symbols represent objects 
would be speedily solved: we could say merely that we are in the 
habit of using such and such signs for such and such things, 
(though we should have difficulty in saying this), and the study 
of the principles of symbolism would be reduced to the compil- 
ing of dictionaries. But this is not all. 

When a group of symbols takes on a meaning through the 
meanings of its constituents, it becomes in a far-reaching sense 
a representative of an object, if it stands for an object. The re- 
lation between a group of symbols and the fact it signifies can be 
likened to the correspondence of a map to a region of which it is 
a partial picture. Each element of the map means a feature of 
the landscape, which is related to other features as the map- 
elements are related to one another. So, each symbol of a group 
means a part of the whole fact signified, a part which is related 
to other parts of the fact as the symbols are related in the group. 
A phrase, a sentence, a mathematical expression, or a complex 
idea is as much a picture of a fact as a map is of a country. The 
difference is that the portraiture is infinitely more subtle. The 
map reproduces the spatial relations of the country by spatial 
relations on a smaller scale. The phrase or sentence reproduces 
the logical relations of the elements in the fact by similar logical 
relations among the symbols. 

A phrase or sentence cannot, then, be arbitrary in meaning. 
It can mean only a fact logically constructed as it is constructed. 
Its form must be the form of the fact for which it stands. 

It is not difficult to discover in what respects a photograph 
or a map resembles its original. The correspondence of the copy 


LOGICAL FORM 43 


with the original is written on the face of both. But the evasive 
features of logical form are not readily made out. What can 
there be in common between the sentence, “‘the sun is shining 
outside my window,” and the fact which the sentence means? 


II 


Symbols, whether they be words, gestures, or ideas, are ob- 
jects. In their rdle as instruments of meaning they are still 
things. A spoken word is a combination of noises distinct from 
other noises. A spoken sentence is a collection of combinations 
of noises with pauses and inflections to indicate its grouping into 
phrases. A written sentence is a collection of marks on a page, 
distinct from other marks and other collections. 

The nature of symbols as objects is not in the foreground of 
perception when they are used to convey meanings. We are only 
dimly conscious of the print when we read; we pierce through it, 
as through a luminous medium, to the meaning. The quality of 
a voice, the sound of a spoken word, fade into the background 
of the mind when we attend to a speaker; we hear only what the 
speaker intends to say. And yet the nature of symbols as ob- 
jects is not completely forgotten in interpreting them, for it is 
this that causes them to be recognized as having a structure. 
There are characters and relations which belong to all objects 
alike and are the most abstract features of their being, and it is 
these characters and relations which the symbols — being also 
objects — reproduce. 

Logical form is the least common factor of all objects. Any 
entity which is presented or thought exhibits logical form, and a 
thing without logical form (if it could be a “‘thing”’) could not be 
brought within the circle of reason. Where logical form ends, the 
presentation of objects, analysis, representation, the rational 
processes, also end; and if any knowledge could remain, it would 
be knowledge by intuition — the pure awareness which gives us 
no objects. 


44 SYMBOLISM AND TRUTH 


The characters and relations that determine logical form ap- 
pear when we ask what it means to be an object or a fact. ““Ob- 
ject”? is the most general of all terms. It applies to everything, 
whether simple or complex; and a definition of “‘object”’ is im- 
possible, since it could not be framed without making use of this 
term. A person, a landscape, a mental state, a quality, a relation, 
an operation — all are objects. The very statement of the fact 
that everything is an object is a tautology. 

“Object” is more inclusive than Aristotle’s “substance” 
(that is, his “first substance’’). By “substance” Aristotle meant 
an individual, which could be a subject of predication or could 
stand in relations to other substances. Objects include not only 
subjects of predication and terms of relations, but also the predi- 
cates and relations which can be attached to subjects and terms. 
Several kinds of objects go together to make up the thing meant 
by “Caesar was the noblest Roman of them all.” Caesar is an in- 
dividual subject; Roman is a predicate; noblest of them all is a re- 
lation — a different kind of object from either of the first two. 
Each of these, as well as the whole fact, is an entity with a dis- 
tinct being; each is an object. 

To assert that a thing is an object is to make the minimum 
statement about it; it is to affirm merely that z is x. But trivial 
as this assertion appears, it is implicit in all knowledge of ob- 
jects; for it informs us that something is singled out, fastened on 
by the attention, and referred to through symbols. 

A fact, which could be represented analytically in a symbolic 
group, is not a bare “this,” an x with no character in particular 
and no relations to other objects. A fact is a complex of different 
kinds of objects: it is a thing with characters, or a number of 
terms in relation; it is a concretion of objects. The whole for 
which “Brutus killed Caesar” stands is a fact. “Rome was not 
built in a day,” stands for another fact. “‘ Fairies have wings,” if 
it stood for anything, would stand for a fact. Taken as wholes, 





LOGICAL FORM 45 


as clusters of objects, facts are themselves objects of an articu- 
lated sort. Unanalyzed objects are the atoms of thought and 
facts the molecules; but molecules can play a part not unlike 
that of atoms, and any given fact can become the foundation of 
more complex facts. 

III 

The first element of structure in a fact is that it is a group — a 
group whose character as a whole is determined by the nature 
and relations of its parts. This concept is fundamental in the 
description of logical form. 

A group, as the term is used here, is any object constituted of 
other objects. The fact meant by (2 + 2) is a group, because the 
whole is a function of the objects meant by 2 and (+). The ob- 
ject signified by “‘the blue sky” is a group determined by the 
objects meant by “blue” and “sky.” (‘‘The” does not stand for 
a constituent of the fact.) ! Similarly, “a precedes b” means a 
group — a fact constituted of the objects a and 6 and the rela- 
tion precedes. Some groups are subjects qualified by predicates, 
others are terms in relation, and still others, terms joined by 
mathematical or logical operations. In short, any object deter- 
mined by other objects is a group. 

The concept of grouping is the same as that of function. To 
say that a whole is a function of its parts is to call attention to 
the fact that it is a group. Every whole is a group and every 
group is a whole; and not only is every fact a group, but every 
collection of symbols with syntactical meaning is also a group, 
whose character as a whole is determined by the nature and re- 
lation of the parts, and whose significance as a whole is a func- 
tion of the significance of the parts. 

It must not be supposed that a disunified plurality of ob- 
jects or symbols is a group in the true sense. There must be a 
determination of the whole by the parts. The relations between 


1 See below, ch. IV, sec. v. 


46 SYMBOLISM AND TRUTH 


the parts, if there are relations other than the general unity of 
the group, are themselves parts or members of the group. Thus 
a between b and ¢ is determined not only by a, b, and c, but also 
by the relation between. This determination of the whole by the 
parts is essential: without this, the plurality of objects is not a 
group. A factual group must be a single fact and a symbolic 
group a single symbol. 

The concept of grouping then presupposes, (1) a plurality of 
objects (members), which may be terms, or characters and rela- 
tions, or both; and (2) the union of these so that the members 
uniquely determine a whole; and in the case of symbolic groups, 
(3) a union of the meanings of the parts so that they uniquely 
determine the meaning of the whole. 

What there is in common between a phrase, a mathematical 
expression, or a complex idea, and the fact it might represent, 
now begins to emerge. Both the symbol and the fact are groups. 
Symbols reproduce groups by groups, as the map reproduces 
spatial relations by spatial relations. But this gives only the 
frame-work of the picture. There are an infinite number of dif- 
ferent symbolic groups and different factual groups, each of 
which can be distinguished by its logical form alone. The possi- 
bilities of reproducing different structures of fact by formally 
distinct symbolic structures are without limit. 


IV 


Every entity, simple or complex, is identical with itself and 
distinct from other entities. Numerical identity and diversity, 
together with grouping, determine logical form because they are 
the most abstract, that is to say the “formal,” characters of 
objects. Differences in logical structure are numerical in nature; 
they are differences in the number of constituents in groups, and 
in the number of groups which are members of groups within a 
whole. Form is in a literal sense number, as the Pythagoreans be- 


LOGICAL FORM 47 


lieved. If, in the apprehension of a fact, everything is disregarded 
excepting the numerical identity and diversity of its elements, and 
their grouping into wholes, what remains will be the logical form. 

Since a simple symbol is not a group, it is not distinguished 
from other simple symbols by its form, though it is distinguished 
formally from any complex symbol. These most elementary of 
signs differ only materially in meaning from one another, that is, 
through the concrete characters of the intentions which attach 
to them or of the objects they mean. At the lowest stage of anal- 
ysis formal distinctions of significance do not appear, €.9.5 
proper names are all of the same form. 

Any analytical representation of an object carries its analysis 
to the limit of the things meant by the simple symbols, and if 
any further analysis is possible, this analysis is not contained in 
the representation. When it is said that the fact meant by “the 
sunshine on the ocean” is composed of the simple elements, swn- 
shine, on, and ocean, these elements are not affirmed to be abso- 
lutely simple, to be irreducible. They are the elementary com- 
ponents of the fact as it is here expressed; the representation 
goes no further in analysis. 

It is evident that the constituents of most facts, as they are 
expressed in symbols, can be further analyzed. If there is a final 
limit of analysis, if some data are absolutely simple, most repre- 
sentations stop short of this limit. A simple symbol represents an 
object with the smallest possible amount of analysis — with a 
zero analysis. These symbols set the scale of reproduction. Just 
as the map may employ one inch for ten miles, so a symbolic ex- 
pression may use a simple symbol for something which is in real- 
ity complex; just as another map may depict the same region on 
a larger scale, so another symbolic group may represent as com- 
plex what is elsewhere represented as simple. But through 
simple symbols alone objects cannot be represented as of differ- 
ent forms. 


48 SYMBOLISM AND TRUTH 


When symbols or objects are grouped, the groups will be 
formally alike or different in several ways: in multiplicity, in 
type, and in the distribution of identical elements (or tautologous 
symbols) within the constituent groups. (These terms are arbi- 
trarily chosen to suggest the concepts they mean.) 

The multvplicity of a group is determined by the number of 
major members. 

However simple or complex the elements of a fact may be, 
these elements, as they are seen through a symbolic expression, 
are of a definite number; and the elements of the fact are corre- 
lated with the constituents of the symbolic group so that for 
each symbol, simple or complex, in the expression there is a cor- 
responding part of the fact, and so that the expression as a whole 
means the fact as a whole. The first layer of facts will be those 
represented by symbolic groups whose elements are all simple 
symbols. “The sunshine on the ocean”’ is such a fact; (2 +8) is 
another such fact. Clearly, neither of these symbolic expressions 
could mean a fact which could not be analyzed into at least three 
elements. The major members of these facts (but only of this 
simplest type of facts) are the unanalyzed objects signified by 
the simple symbols. The number of these objects determines the 
multiplicity of the fact, and the number of simple symbols, the 
multiplicity of the symbolic group.' But the major members are 
not always simple symbols or the objects meant by simple sym- 
bols; the major members may be complex, and the multiplicity 
of the expression or the fact will not then be fixed by the number 
of simple components. 

Primary facts, facts of the lowest layer, may enter as wholes 
with other constituents to form new facts; and these will belong 
to a second layer. At least some of their constituents will be 


1 The article, “‘the,”’ does not represent a constituent of the fact. With it 
must be classed “a,” “any,” “some,” “every,” “each,” and “‘all.”’ See below, 
ch. IV, sec. v. Similarly, “‘not” does not stand for a constituent of a fact. See 


below, ch. VI. 





LOGICAL FORM 49 


themselves complex, and will be signified by groups within 
groups. This gives the second dimension of logical form — the 
type of the group. Horizontally, so to speak, a form is deter- 
mined by the number of its major members; vertically, by the 
number of groups included within groups. 

The sentence, “‘the sunshine on the ocean pleases me,’’ repre- 
sents a fact whose constituents are not unanalyzed objects signi- 
fied by simple symbols. One of the constituents of this fact is 
itself an analyzed fact reproduced by a symbolic group. The 
whole includes a subordinate group, “the sunshine on the 
ocean,” and this is combined with the things meant by “pleases” 
and “‘me” to form a fact of higher type. The secondary fact 
therefore contains a primary fact as one of its constituents. 

Now the sentence, “‘I am happy because the sunshine on the 
ocean pleases me,’”’ means a fact of a still higher type. The 
secondary fact, “the sunshine on the ocean,” has become an 
element in a new whole through its union with the things meant 
by “I,” and by “‘happy,” and “because.” (The copula, “is” 
and its variants, is a sign of assertion; its function is unlike that 
of any other sign.)} 

Facts combine and recombine in this way, reaching higher 
and higher levels of complexity. The result is a multitude of new 
logical forms — new combinations of symbols with symbols and 
objects with objects. 

The major constituents of such facts and symbolic groups are 
the facts and groups which enter immediately into the whole 
without being constituents of sub-facts or sub-groups. All the 
other elements are minor constituents. The fact, ““I am happy 
because the sunshine on the ocean pleases me,” contains as 
major constituents the two subordinate facts, “I am happy” 
and ‘‘the sunshine on the ocean pleases me,” and these are 
joined by the major relation “because.” These subordinate 


1 See below, ch. V, sec. xiii. 


50 SYMBOLISM AND TRUTH 


facts in turn contain their major constituents, which are the 
minor constituents of the larger fact. The analysis proceeds as 
far as the facts composed of elements meant by the single words, 
and these facts contain only major constituents. Their elements 
are the basic materials of the structure. 

The type of an expression or fact is therefore determined by 
the number of groups within groups. An expression or fact of the 
first type has no members which are groups. (2 + 2), (a — b), 
France fears Germany, are of the first type. An expression or fact 
of the second type will include as a major member at least one 
(or more than one) group of the first type; e.g. (a (b—c)), France 
fears a new war. The other major members of such a fact may, 
as in these cases, be things meant by simple symbols, or things 
meant by groups of the first type, e.g. ((a + b) — (e+ d)). 
In general, an expression or fact of the nth type will include as a 
major member at least one (though it may include more than 
one) group of the n — Ist type; and as a consequence, it will in- 
clude as minor members groups down to the {st type. 

In determining the multiplicity of a group, its type must be 
taken into consideration, for it is the number of major constitu- 
ents (the members entering immediately into the whole without 
being constituents of sub-groups) which establish the multiplic- 
ity, and these may be of a higher type than the first. Thus 
((a — b) — (b— ¢)) has only three major members, that is, the 
operation (— ), and the complex terms (a — 6) and (b — c). Its 
multiplicity is not determined by the number of simple symbols 
or unanalyzed elements. 

If facts of a secondary, tertiary, or higher type are alike both 
in their horizontal and vertical dimensions, they will be of the 
same form. This means that they must have the same number of 
major constituents, and that each of these constituents in the 
one must be constructed of groups within groups exactly as is a 
corresponding constituent in the other, and vice versa. 


LOGICAL FORM 51 


vi 


Language exhibits the form of the facts it signifies much less 
clearly than do some other kinds of expressions. This is because 
the grouping of words into phrases and sentences is brought 
about by grammatical rules, which are felt rather than made 
evident in the group. Nevertheless, every phrase or sentence of 
any complexity is organized into groups within groups, as is also 
the fact for which it might stand. The major verb or connec- 
tive shows the major lines of cleavage; it connects the major 
symbolic members. These in their turn are composed of minor 
groups, joined by minor verbs and connectives. Punctuation 
plays a part here; commas, semicolons, dashes, brackets, peri- 
ods, etc., indicate what symbols are to be taken together. These 
are signs of syntax. 

Signs of syntax are secondary signs — signs of symbolism 
rather than signs of objects. They do not refer to elements in the 
fact for which the symbolic group might stand. They refer 
merely to the symbols. They mean that the symbols with which 
they are placed are to be treated as a group; that these symbols 
constitute a significant whole. 

Mere juxtaposition of symbols, although it is usually a sign 
that they are a group — and is the only sign of syntax in the 
system of mental images — is not a sufficient sign in most sys- 
tems. There must be additional ways of indicating the grouping. 
In language there are at least four signs of syntax: classification 
of words and expressions as parts of speech; inflections, case 
endings, genders, etc.; position; and punctuation. The signs 
of syntax in algebra, arithmetic, and all quasi-mathematical 
groups, having been invented for convenience, are simpler than 
those of language. The form of an algebraic expression is indi- 
cated by parentheses; thus ( (a + 5) X c) is plainly similar in 
grouping to ( (d — e) X f). These expressions are of the same 
logical form — a form which can be described as a group of 


52 SYMBOLISM AND TRUTH 


three major members, one of which is a group of three unana- 
lyzed major members. The parentheses are the signs of syntax, 
that is, the punctuation of these mathematical expressions. 

In Messrs. Whitehead and Russell’s Principia Mathematica, 
the signs of syntax are dots; the larger numbers of dots indicate 
the more inclusive groups, the smaller numbers, the minor 
groups. Any signs of syntax must be such that they preserve the 
integrity of the groups and show what groups are members of 
other groups. 

As the forms of facts and the symbols which represent them 
grow more complex, verbal descriptions become more lengthy. 
There is a simpler manner of exhibiting forms. If letters are 
taken to stand for the elements of a fact (or a symbolic group) 
and parentheses as signs of grouping, any logical form can be 
presented in a general schematism. ((a R 6b) S c) exhibits the 


form of the two algebraic expressions given above, ((a + 6) Xc) - 


and ((d — e) X f), and of the facts for which they might stand. 
It also exhibits the form of the sentence, “‘Brutus was the friend 
of Caesar,” and of the fact which this signifies. This sentence, 
and the fact, fall into major and minor groups as follows: (Bru- 
tus was (the friend of Caesar) ), and except for spatial order, 
which can be disregarded here, the symbols are grouped exactly 
as is the expression ((a Rb) S c). 

The use in this general schematism of capital letters for some 
of the group-elements should be noted. Wherever there is a com- 
bination of elements, the terms combined must be distinguished 
from the relation or operation which unites the terms. Qualities, 
relations, and operations enter into, modify, and give unity to 
groups of terms in a peculiar way, and they can be classed to- 
gether as elements of unity, which are distinguishable from the 
terms they unify. A quality is a modifier (or element of unity) 
in a group of one term, ¢.g., “‘the white knight,” which is of the 
form (fa). A relation appears in a group of several terms, e.g., 


LOGICAL FORM 53 


“‘a between 6 and c,” and an operation may enter in a group of 
any number of terms. The capital letters in this general repre- 
sentation of logical forms stand for symbols or elements of 
unity, while the small letters stand for terms. 

Similarity of form between groups, whether it be between 
facts, between symbols, or between symbols and facts, can be 
shown by correlating them as follows: Each major constituent 
of the one must be made to correspond with one and only one 
major constituent of the other, and vice versa; and if these con- 
stituents are groups, each of their major members must be made 
to correspond uniquely, and so on, down to the elements signi- 
fied by the simple symbols. This correlation will give a perfect 
parallelism of members, both horizontally and vertically. (Pos- 
sible complexities in the element or symbol of unity are neg- 
lected. There will be at least one element or symbol of unity in 
every group, and although this may be complex, it can be 
treated as one — as the element of unity.) ! 

When a symbolic group stands for a fact, such a correlation of 
the group with the fact is set up by the relation of meaning. 

This parallelism of groups, of terms and elements of unity, of 
complex and simple constituents, makes possible a comparison 
of the structure of groups without counting the number of the 
members or the layers of superimposed groups. We do not need 
the concept of the number-series in order to apprehend similar- 
ities and differences of form, but merely the concept of one-to- 
one correspondence, on which the number-series is based. The 
eye effects such a correlation in observing that ((Rab) Sc) and 
((Qde) Mf) are of the same form. 


VI 
Symbolic groups thus constructed could not have a wholly 
arbitrary meaning; the principle of syntactical meaning makes it 


1 See below, ch. III, sec. xvii, for the additional differences of form intro- 
duced by the complexity of the element of unity. 


54 SYMBOLISM AND TRUTH 


necessary that in form at least they must reproduce the objects 
they might signify. Given significant simple symbols and a logi- 
cal form, and the meaning of the whole will be determined by 
the meanings of the simple symbols and by the logical form. It 
will be possible to analyze the fact meant (if there is a fact) into 
groups and simple elements parallel to those of the symbolic ex- 
pression. 

Any fact can be analyzed in a number of different ways. Its 
lines of division and grouping run in different directions, de- 
pending on the elements chosen as the basis of the analysis. All 
the possible ways of stating the same fact will represent the dif- 
ferent lines of structure, the different analyses. The fact, “‘a is 


> 


between b and ec,” is the same (if a, b, and c mean the same 
things in both cases) as “a is to the right of b and ¢ is to the 
right of a.’ ““Caesar conquered Gaul” and “the first Emperor 
of Rome triumphed over the region which is modern France and 
Germany,” are different analyses of the same fact. No fact and 
no object is exhausted by a single analysis. The analysis directs 
our attention to certain aspects of the fact, but other aspects of 
it remain untouched. There is no single logical form which is 
peculiarly the form of any one fact. 

Statements of the type, “a is y,”’ where “‘is”” means “‘is identi- 
cal with,” tell us that a single fact permits different analyses; a 
large part of our knowledge is embodied in observations of dif- 
ferences of structure in the same fact. “2 + 3 is 5,” for example, 
informs us that the object which we signify by “5” can be de- 
composed into the constituents meant by “2” and “3” and 
**plus.”’ And if statements of identity were trivial, as they are 
sometimes said to be, much of our knowledge would be trivial. 
It is doubtless of no interest, excepting as a case of a general 
logical principle, to know that “a is a,” and only of slight inter- 
est to know that “a is b”’; but it is of great interest to know that 
the same fact can be stated in different ways, that a single ob- 
ject exhibits a variety of logical forms. 


LOGICAL FORM 55 


VII 

We have yet to consider the third element of form — the dis- 
tribution of identical members, or tautologous symbols, among 
the constituent groups of a fact or a symbolic expression. 

Meanings must have a certain fixity and continuity. If sym- 
bols were fluid and capricious in their references they would be 
of no use, for we should never know exactly to what they re- 
ferred. In any discourse symbols recur, they appear again and 
again, and on each recurrence they are given the same interpre- 
tation. 

Now, strictly speaking, a repeated symbol is not the same ob- 
ject. The sound “bird” uttered to-day is not identically the 
sound “‘bird”’ uttered to-morrow. The image of my friend which 
is in my mind now is not identical with the image of him which 
was in my mind an hour ago. Therefore a symbol is something 
more than a single object which comes before the mind, takes on 
meaning, and disappears. Recurrence is of the essence of sym- 
bols. The same word may enter many times in one sentence and 
many more times in a paragraph. A number or letter may reap- 
pear in different parts of a single mathematical or logical ex- 
pression. We cannot say that the word, the number, or the 
letter is the very same in each instance, but all the instances are 
like enough to be classified together, though each is a distinct 
object. The symbol is all the cases of its own recurrence. 

A symbol then is not a single object, but a class of objects. 
Symbols are the same symbol only if they exhibit a generic sim- 
ilarity as objects, and they are distinct symbols if they exhibit 
a generic difference. Thus a and 6 are distinct symbols because 
their contours as marks on a page are different, while a and a (if 
they are not ambiguous) are the same symbol because their con- 
tours are alike. When we select an object as a symbol, we fasten 
on one or more of its concrete characters, and only objects with 
these characters are treated as the same symbol, while objects 


56 SYMBOLISM AND TRUTH 


of different characters are treated as distinct symbols. The char- 
acters that give generic similarity or difference to symbols may 
be any characters whatsoever. In European languages, for ex- 
ample, differences of pitch do not differentiate spoken signs, 
while in Chinese they do. 

Apart from ambiguity, which must be dealt with as a special 
factor, a recurrent symbol always means the same object. Re- 
current symbols are tautologous; they are not symbolically dis- 
tinct and yet they are not identical as objects. But when it is 
said that tautologous symbols mean the same object, this 
“‘sameness”’ is not the sameness of similarity. The object is 
identically the same. Identity is that which makes an object one 
and unique. No two objects which are alike can be identical, for 
they are two and must therefore be at least numerically distinct. 
The recurrent instances of a symbol, though they are alike, do 
not signify objects which are merely alike. They mean an identi- 
cal object. 

The principle which gives rigidity to the meanings of symbols, 
that is, that the same symbol, if it stands for an object, stands for an 
identical object, is the principle of identity. Not only is a symbol 
a class of objects; it is a class of objects whose meaning is unique. 
Symbols which have different meanings are different symbols; 
it is impossible that the same symbol should have more than one 
meaning. 

The attempt to interpret a symbol in more than one way 
gives rise to psychological ambiguity or equivocation; and this 
must be distinguished from the logical ambiguity of a phrase 
such as “a man” or “some man.” Logical ambiguity is useful in 
thought, but equivocation makes precision of conception or 
statement impossible.! Equivocation is eliminated only when 


1 It is true, however, of logically ambiguous symbols, as of all symbols, 
that they follow the principle of identity. They can have only one meaning. 
The variable, ‘a man,” if it is given a value, can be given one and only one 
value. 


LOGICAL FORM 57 


the equivocal symbols are treated as distinct. Though the 
spoken words “read” and “red” do not differ in their character 
as objects, they are different symbols in the sentence, “I read 
a red book,” and they cannot be construed as the same without 
a distortion of the meaning. Needless to say, images are even 
more open to ambiguous interpretations than words. 

Every symbol, then, presupposes the uniqueness of its own 
meaning, and this is what the principle of identity, a is a, tells 
us. It states that a, wherever it occurs, is to be interpreted by 
one and only one object; and if a is significant, but stands for no 
object, the principle tells us that if a represented an object it 
could be one and only one. 

This principle is therefore a general rule of symbolism. 
Phrases such as “the round square” and names such as “ Phoe- 
bus Apollo,” which refer to no existent objects, follow the law of 
identity no less than do phrases such as “the present king of 
England” or names such as “‘ Julius Caesar.” “A round square” 
as ““a round square,” “Phoebus Apollo” is “Phoebus Apollo,” 
in the sense that each of these symbols is to be interpreted in 
one and only one way, in the sense that each has a meaning of its 
own different from that of all other symbols not expressly de- 
fined to have the same meaning. “Round square” plays the 
same part in the symbolism, wherever it appears, as “round 
square’; instances of this symbol can replace one another in any 
expression without altering the meaning of the whole. In short, 
as a general rule of symbolism, a is a, states that a is the same 
symbol as a. It declares an intention to interpret a uniquely. 
The very conception of a symbol as distinct from other symbols 
and the same in all its instances demands that its meaning be 
unique. 

The principle of identity can also be interpreted in another 
way, that is, as a statement of fact about objects; but this sec- 
ond interpretation presupposes the first—the interpretation as 


58 SYMBOLISM AND TRUTH 


a rule of symbolism. When a stands for an object, a 7s a asserts, 
not merely that a and a are the same symbol, but that the ob- 
ject meant has an identity, that it is an object. This is the 
existential as distinguished from the symbolic interpretation of 
the principle of identity. And if a is a variable, so that it means 
any object, a is a affirms that “any object is identical with 
itself.” 

Clearly, such a statement of identity is false if it refers to no 
object; it is not true that “a round square is a round square” in 
the sense that round squares have identity. However, “a 2s a,” 
man 7s man,” could not be asserted as 


99 66 


“Caesar is Caesar, 


99 «66 > 


a,” “Caesar,” “‘man,”’ were 


“«¢ 


existential propositions unless 
construed as the same symbols in each case. It must be assumed 
that the meaning of a symbol is unique if any object is affirmed 
to be identical with itself; but it is not necessary to assume that 
the symbol stands for an object in order to assert that it can 
have one and only one meaning, for this latter rule is a condition 
of its use, whether or not it stands for an object. 

Distinct symbols, symbols whose characters as objects are 
dissimilar, may be equivalent in meaning; they may stand for 
an identical object, or if they stand for no object, they may be 
treated as indistinct in meaning. This treatment will not make 
them the same symbol, for symbols must be alike as objects to 
be the same. Thus “red” and “vermilion” are distinct symbols 
with the same meaning; but they are not tautologous or recur- 
rent instances of one symbol. Such equivalences may be equiva- 
lences by definition only, and they will then be statements of 
special intentions in the use of symbols: the equivalence “a is 
b” tells us that a and b can be substituted for one another 
wherever each occurs. This equivalence is a valid definition, but 
as an assertion of fact it may be false. Thus “Titania” is “the 
queen of the fairies’; but there are no fairies and no Titania. 
Definitions do not require the existence of an object defined, for 





LOGICAL FORM 59 


they are primarily concerned with the use of symbols, and a 
valid definition may be false as a statement of fact. 


VIII 


The proposition, a ts a, when it means that any object is iden- 
tical with itself, is true without exception. There is nothing of 
which we can speak that is not self-identical. 

The concept of the identity of an object is said by Hume to be 
a fiction. Objects weave themselves in and out of experience as 
do threads in a tapestry, and it is difficult, if not impossible, to 
know that a thing which appears the same is really the same. 
But the entire fabric of thought would fall apart if we did not 
assume that an object fixed as a thing meant can remain identi- 
cal with itself. 

Putting aside the question of the reality of these self-identical 
objects, we must suppose that objects — for knowledge at least 
— stand still long enough to be referred to and re-referred to, 
for if this were not so nothing could be represented. All objects, 
including symbols themselves, would flow together; there would 
be no differentiation in knowledge. Nothing would remain itself 
to be an instrument of significance or a thing signified. We could 
not relocate anything we had previously known, and we should 
be helplessly blown about by the winds of change. Thought must 
view the world as if it were made up of points and lines of iden- 
tity, which combine with and intersect other points and lines, 
but which do not cease to be themselves. 

The nearest approximation to a definition of an object 
(though it is not a definition) is this: that an object is anything 
with the twin characters of identity and diversity; and this 
statement is equally true of subjects, predicates, terms, rela- 
tions, and complex wholes. A universal such as whiteness has its 
identity ; it is something because it is identical with itself and dis- 
tinct from other things — from other universals and from each 


60 SYMBOLISM AND TRUTH 


of its own instances. A particular, referred to by “this white ob- 
ject,” for instance, is more obviously self-identical and diverse 
from other objects. These two formal characters are the sources 
of unity and plurality in the world. Wherever there is an object 
it must be a unity — one and identical with itself — and there 
must be other such unities from which it is distinct. 

It would be natural to suppose that the identity and diversity 
of objects arise through special qualities or predicates, or 
through sets of relations, which attach to objects. But if we at- 
tempted to carry this idea forward, we should then have to ex- 
plain why these predicates or sets of relations are unique, why 
they are themselves and not something else; and we should have 
made no advance. Identity and diversity are irreducible con- 
cepts, and the argument which shows most convincingly that 
they are indefinable is that the characters and relations in terms 
of which they could be defined (if at all) must themselves be 
assumed to be self-identical and diverse from all other characters 
and relations. 

When symbols copy the forms of objects, they reproduce the 
identities and diversities among objects, together with the 
grouping of these identical and diverse elements into wholes. A 
symbolic group is a black and white portrait of a fact; it leaves 
out everything but the identities, diversities, and groupings of 
the original. But the representation of the identities is a projec- 
tion, rather than a copy; for an identical element, entering and 
reéntering in several places in a fact, is signified not by an iden- 
tical symbol but by a recurrent symbol. The identical element is 
projected into the medium of time (or space) in the representa- 
tion. What is a single thing in the fact is reproduced by a series 
of similar things in the significant expression, that is, by a num- 
ber of instances of the same symbol, and the convention by 
which this projection is effected is the principle of identity. For 
this principle affirms that if the instances of a symbol stand for 





LOGICAL FORM 61 


an object, this will be a single object. Tautologous symbols in 
the representation stand for identities in the fact. 

An identical element may enter in many different ways in a 
fact. Many different complexes may be centered about the same 
object to constitute a whole, and this identical component need 
not be recurrent in a spatial or temporal sense. ‘‘ Hamlet’s father 
was Hamlet’s Nemesis,” states a fact in which the same object 
enters in two different ways: the whole fact is composed of two 
major groups with an identical constituent in each. It is of the 
form ((a 8 b) Q (aS c)). Such a fact is like a number of inter- 
secting lines; it is made up of groups with common members. 

Still other facts are reflexive they; arise through relations 
which hold between a term and itself. The identical element in a 
reflexive fact enters as a major constituent at least twice in the 
same group. “‘Hamlet feared himself”’ stands for a reflexive fact, 
for the fact “‘Hamlet feared Hamlet,”’ which is of the form 
(a R a). Strictly speaking, we ought not to say in such a case 
that the fact is reflexive; rather, it is the symbolic expression 
which is reflexive, for here again the expression does not exactly 
copy the fact. The fact has only one term, while the symbolic 
group has two, though these two are not distinct. The fact is 
really of the form (Sa); and it is through the tautologous re- 
currence of a symbol that we can represent it as of the form 
(a R a). Thus what is in fact a quality (for a quality is an ele- 
ment of unity attached to a single term) is symbolized as a rela- 
tion. “Napoleon loved Napoleon” means the same thing as 
“Napoleon was egotistical’’; and the possibility of representing 
an identical term through a recurrent symbol enables us to treat 
this quality as a relation — a relation between a term and itself. 

In determining the multiplicity of such reflexive expressions, 
the different instances of the same symbol must be reckoned as 
separate terms or members. Thus (a R a) has two terms and is 
the same in multiplicity as (a R 6). (Qaab), which is the form of 


62 SYMBOLISM AND TRUTH 


“*a gives b to a,” where “gives to”’ is a single relation, has three 
terms and is the same in multiplicity as (Qabc), which is the 
form of “a gives b to c.” It is clear that the multiplicity of the 
fact meant by these reflexive groups is not that of the symbolic 
group; a fact of a lesser multiplicity is represented, through 
tautologous symbols, as of a greater multiplicity. 

The manner in which an identical object appears and reap- 
pears as a component in a single fact is the third distinctive fea- 
ture of logical form; and facts or symbols of the same form must 
correspond not only in the number of their constituents, but 
also in the distribution of identical elements or tautologous sym- 
bols among the groups. Thus (a R a) and (0 S 6) will represent 
facts of the same form, which is that of “Napoleon loved Na- 
poleon” or “Hamlet feared Hamlet.” The symbols ((a R b) S 
(a Rc)) and ((eQf) L (e Q g)) will stand for facts of the same 
form — facts such as that signified by “Juliet’s love caused 
Juliet’s doom.” It is easily seen that the appearance of an identi- 
cal element in different ways in a fact leads to many new vari- 
eties of form. 

These identical elements may also be represented by distinct 
but equivalent symbols; and here too the symbolic group does 
not exactly portray the fact, but contains more distinct mem- 
bers than there are distinct elements in the original. “‘Hamlet 
mistrusted himself” is composed of three distinct symbolic 
members, (“‘Hamlet”’ and “‘himself”’ are symbolically distinct), 
while the fact to which this expression refers contains only two. 
The expression is redundant in form. Such a group can always 
be reduced to a more exact copy, or projection, of the form of 
the fact by replacing the equivalent symbols by instances of the 
same symbol; and this is what is done in interpreting the expres- 
sion. Its meaning is the same as that of ‘‘Hamlet mistrusted 
Hamlet.” 

The distribution of tautologous symbols or identical elements 





LOGICAL FORM 63 


in the constituent groups of a symbolic expression or a fact 
takes a place of equal prominence with multiplicity and type in 
the determination of logical forms. For the distinction between 
a reflexive and a non-reflexive group, or between a group whose 
sub-groups contain common members and one whose sub-groups 
contain no common members (or differently distributed ones), 
is a formal and not a material distinction. 


IX 


Among the more important differences of form which have 
not been mentioned are those of order — the difference between 
““a precedes b” and “‘b precedes a.’’ Order requires no new con- 
cepts; it is determined by grouping alone.! 

In the present chapter we have shown how logical form arises 
from the grouping of self-identical and diverse objects into facts, 
and of tautologous and distinct symbols into significant wholes. 
The structure of a symbolic expression copies the structure of 
the fact which it means, or might mean, through its grouping. 

The three chief features of logical form are: (1) multiplicity, 
(2) type, and (3) the distribution of tautologous symbols or 
identical elements within groups. The multiplicity of a group is 
determined by the number of major constituents, recurrent sym- 
bols being counted as separate constituents; the type by the 
number of groups within groups down to the elementary con- 
stituents. The major members of any group are those which en- 
ter immediately into the whole and are not members of minor 
groups. These major members may be simple or complex. 

The distribution of identical elements in a fact is not exactly 
reproduced in the symbolic group; these identical elements, 
which may not themselves be recurrent, are represented by re- 
current symbols. Groups of like form must correspond with one 
another in this respect, as well as in multiplicity and type, and in 


1 See below, ch. III, sec. xiv. 


64 SYMBOLISM AND TRUTH 


the multiplicities and types of their sub-groups, down to the 
simple constituents. The principle which permits us to represent 
identical elements in a fact by recurrent or tautologous symbols 
is the principle of identity. A symbol is not a single object but a 
class of like objects, and in any or all of its instances its meaning 
is unique. The principle of identity tells us that a symbol can 
have one and only one meaning; and this is the case whether or 
not the symbol stands for an object. The principle of identity is 
therefore primarily a general rule of symbolism, but it can also 
be interpreted as stating a fact — the fact that “any object is 
identical with itself.” Its use in this sense presupposes its valid- 
ity as a rule of symbolism; but a statement of identity which is 
false as an affirmation of the existence of a self-identical object 
is valid as an affirmation that the same symbol is always used in 
the same sense. Distinct symbols may be defined as equivalent 
in meaning, regardless of their reference to existent objects. 
Identity and diversity are indefinable. 

Equivocally interpreted symbols are distinct, for a single 
symbol can (by the principle of identity) have one and only one 
meaning. 

Simple symbols are not distinguished from one another by 
their form, for they are not groups. They represent objects with 
a zero analysis; they set the scale of reproduction; but the ob- 
jects which they represent as simple may be in reality complex. 
These objects are taken as simple merely for the purposes of 
representation. Any single fact permits many alternative analy- 
ses; it may have many different forms; and no analysis exhausts 
a fact. 

The concept of a group, on which the notion of structure rests, 
is the same as the concept of function. A group is (1) a plurality 
of objects and (2) a whole determined by its parts, and the rela- 
tions between them; and (3) in the case of symbolic groups, 
the meaning of the whole is determined by the meanings of the 





LOGICAL FORM 65 


parts. Signs of syntax—punctuation, parentheses, etc.— indicate 
what symbols are to be taken together as significant groups. 


Logical forms can be represented in a general schematism 
through letters grouped in parentheses. Thus (Rab) and (Sabc) 
differ in multiplicity but not in type; ((Sab) Q (Ldf)) and 
(Rab) differ in type but not in multiplicity; ((Sab) Q (Zdf)) and 
(Sabc) differ both in multiplicity and in type; and ( (Raab) Sa) 
and ((Qabc) Sd), though they are alike in every other respect, 
differ in the distribution of identical (or tautologous) elements. 
Comparisons of form, since form is numerical in nature, can be 
effected by a one-to-one correlation of groups without the use of 
the concept of the number-series. 

The capital letters in this schematism signify elements which 
perform a unique function in each group, elements of unity, that 
is, relations, operations, qualities; and these must be distin- 
guished from the terms related, qualified, or operated on. 

Logical form is so woven into speech, and even into the play 
of the imagination, that it is impossible to utter a phrase or call 
to mind the images of a past or future experience without throw- 
ing them into the forms we have described. To say that a fact is 
not of logical form is to say that no significant assertion can be 
made about it; it is to say that it is not a fact. Such a “‘fact”’ is 
placed beyond the reach of thought or rational experience. 


CHAPTER III 


UNIVERSALS AND INDIVIDUALS: ORDER 


I 


Every presented object has two aspects: it is both universal 
and individual, a “‘what” and a “‘this,’’ an essence and that in 
which an essence is embodied; and we have not completely de- 
scribed logical form until we have considered this cleavage of 
the objects of knowledge into universals and individuals. 

Objects are not perceived without their natures and their re- 
lations to other objects being also perceived. Each is a “this” of 
some quality, or a “this” related to something which is diverse 
from it; and the minimal cognition of objects — a perception of 
the distinctness of “this” and “‘that”’ — contains a universal, 
for distinctness is a universal. If one attempts to grasp the 
“this” without its qualities or relations, it is no longer a “‘this”’; 
it becomes so vague as not to be known even as “‘something-or- 
other.’’ We lose it in the pure awareness where there is neither 
“this” nor “‘that.’’ And yet no object is perceived as a pure 
quality or relation. I am not presented with sheer whiteness or 
betweenness or beforeness. A perceived universal is perceived in 
something, as qualifying a subject or as relating terms; and this 
subject or these terms are not themselves merely qualities or re- 
lations. There is something in perception to which the universal 
is united. The universal is perceived as individualized. 

No distinction has given rise to wider divergence of opinion. 
Plato dismisses the imponderable something in perception which 
is not universal as an element of imperfection; but this indeter- 
minate something reappears as the unintelligible “matter” or 
absolute non-being of his cosmology. In Aristotle’s metaphysics 





UNIVERSALS AND INDIVIDUALS 67 


the same imponderable, far from taking the form of absolute 
non-being, becomes infinite potentiality, infinite possibility of 
being; but Aristotle finds no actual being which is not also uni- 
versal. The nominalist, on the one hand, affirms that only the 
individual is real; and the realist — the extreme realist — that 
only the universal is real. But if with the Platonic realists we 
turn our minds away from the things of perception and deny the 
reality of individuals, we are still confronted with the facts of 
perception; and though these facts are proclaimed to be “‘opin- 
ion”’ or “illusion,” the duality of universal and individual, in a 
very persistent form, continues in knowledge. Nor does the 
denial of the reality of universals make them any the less im- 
portant as phenomena of knowledge. 

The distinction between the “‘ what” and the “this” is omni- 
present in knowledge whether or not it is in reality. 


II 


One of the paradoxes of knowledge is that having made the 
distinction we attempt to escape from it by describing the in- 
dividual in universal terms. 

My house is built of brick and stands on a hill. I return to it 
after a day’s absence to find that the red walls still top the hill; 
but what I recognize are the characters and relations, and not 
the individual thing—my house. If I try to describe its individ- 
uality, I find that this dissolves into new characters and rela- 
tions; it continually recedes from my grasp. I have embarked on 
an apparently endless process of distinction and characteriza- 
tion. Predicates split off from the individual and leave it intact. 
The very name of an individual takes on universal significance; 


1 This distinction between the universal and the individual is not the same 
as the distinction between essence and existence, which Mr. F. H. Bradley 
describes as the separation of the “‘what” from the “‘that.”’ (See F. H. Brad- 
ley, Appearance and Reality (1893), ch. xv.) An individual, a “this,” may or 
may not be in existence, yet its individuality, its “this,” will be distinct from 
its nature, its ‘‘ what.” 


68 SYMBOLISM AND TRUTH 


we speak of ‘‘a Solon” or “a Solomon.”’ From “Caesar”’ is de- 
rived “Caesarian’’; and we refer to “Caesarian pomp” or 
“‘Caesarian power.” What was “Caesarian” in Caesar was not 
then the individual himself, but a quality of the individual. A 
distinction of the “what” from the “this”? always leaves a 
“this” in which a new “what” can be distinguished. 

The problem of whether the individual is completely de- 
scribable in universal terms is one form of the general problem 
of determinism. Laws are descriptions of phenomena; and de- 
terminism in one sense means that all phenomena follow laws — 
that they can be described in universal terms. And if the task of 
knowledge is completely to describe its objects through laws — 
to reach a “specific essence”’’ of everything — then knowledge 
defeats its own purpose by admitting the distinction between 
universals and individuals, unless it can finally abolish the dis- 
tinction and identify an individual by its predicates and rela- 
tions. 

The pursuit of the “specific essences”’ of individuals makes it 
equally plausible to assume either that individuals are not iden- 
tified by their predicates and relations, or that they are. The 
question raises a genuine antinomy. The fact that every individ- 
ual can be more and more fully characterized, that the margin 
of confusion with other individuals is narrowed as more and 
more predicates are affirmed of it, seems to be evidence that a 
sufficient number of predicates — perhaps an infinity — would 
exhaust the individual; but it is equally good evidence that no 
predicates exhaust it. If I say of the tree beside my window that 
it is a pine with bark of grayish green, that it stands six feet from 
the house and thirty feet high, that its branches are covered 
with moss—if I describe it by these and a thousand other pred- 
icates, it is still that to which the predicates attach, and I can 
find more predicates. The universals are like intersecting lines at 
a focus, excepting that the lines determine a point, while the in- 





UNIVERSALS AND INDIVIDUALS 69 


dividual seems to lie outside all intersecting universals; and 
there is no contradiction in assuming that another individual 
might have all the same predicates and relations. 


iI 


But is an individual not determined by its spatial and tem- 
poral relations? Is it not impossible that two individuals should 
be in the same place at the same time? And if we can know where 
and when an individual is, have we not described it beyond all 
confusion with other individuals? 

There is in perception a direct apprehension of the numerical 
diversity of individuals — of the “this” of one object and the 
“that” of another — and this perception, taken together with 
the perception of change, is the basis of the concepts of space 
and time. This is the sole manner in which an individual is 
known as distinct from other individuals. Of two peas which are 
exactly alike in every respect the only difference I can perceive 
is a bare numerical diversity, which is not a diversity of char- 
acters and relations, but a pure difference of individuality. To be 
thus perceived as distinct, individuals must be copresent, and 
they must neither change nor be in motion. The “this” and the 
“that”? must form a changeless whole of perception. This nu- 
merical diversity may, moreover, be given as a relation between 
several terms; the distinctness may be one of three or four, or 
possibly half a dozen, individuals. 

If, along with this perception of numerical diversity, goes a 
perception of change, the phenomenon is ambiguous; there is a 
question as to whether a “this” which is present at a later stage 
of the change is the same as the “this” of an earlier stage. The 
two individuals are not perceived as distinct, since they are not 
copresent; and yet they are not perceived as the same. Imagine 
a uniform field of gray before the eyes and suppose that this be- 
comes green and then red. Is the “this” of the object the same 


70 SYMBOLISM AND TRUTH 


beneath its changing aspects, or is each perceptible difference of 
quality joined to a different “this’’? Is the individual momen- 
tary, or does it persist through time? 

Change, introducing as it does the element of time, is open to 
two interpretations: it may be that the qualities and relations 
alone are different, while the individual remains the same; or 
that both are different. The change may be like the flow of a 
river, a continuous displacement of one individual by another, 
or like the approach of two moving bodies, an alteration of 
qualities and relations without the entrance of new individuals. 
From one point of view it seems that in each moment of time 
individuals are destroyed and replaced by new individuals, 
while from another point of view it seems that the individual 
must persist, at least for a brief period of time. How are we to 
recognize either the destruction or the persistence of an individ- 
ual? How are we to know that the “‘this”’ of one situation is the 
same as the “this” of another? We can interpret our memory of 
the historical continuity of our own selves as the perception of 
an individual persisting through time; but if this is what we 
mean by the perception of a persisting individual, certainly we 
know only one individual in this way. Whenever we believe that 
we are perceiving in the outer world an historically continuous 
individual, whose qualities and relations alone are changing, it 
is always possible that Descartes’s playful demon is at work, 
substituting distinct individuals along with the different quali- 
ties and relations; and if a changing object is viewed at remote 
times, it becomes increasingly difficult to believe that the indi- 
vidual persists through change. 

Individual objects can be perceived to be distinct and self- 
identical only if they are held together in a single whole of per- 
ception. But this does not amount to the scholastic principle of 
individuation — that the place of an individual at a certain 
time determines its individuality. This principle reverses the 





UNIVERSALS AND INDIVIDUALS 71 


true order-of the concepts of spatio-temporal position and in- 
dividuality. The reason why individuals cannot be in the same 
place at the same time is that their numerical diversity and 
self-identity as individuals — apprehended in a single whole of 
perception — gives us the meaning of “the same or different 
places at the same time.” 

If there were any such thing as an independent space-time, it 
would probably be true that position in space and time would 
identify individuals. But it is impossible to view space and time 
as independent entities with reference to which objects take 
positions. Space and time are functions of objects; there are 
“places” in space and “moments” in time because individuals 
are self-identical and distinct. If I wish to show where and when 
an individual is, I must do so by referring it to other individuals 
from which it is numerically diverse, and so on, ad infinitum. 
The spatio-temporal relations of individuals are not describable 
without the use of other individuals as a frame of reference, and 
since the individuals which constitute this frame of reference 
are not themselves identifiable by their spatial and temporal 
codrdinates, no individuals are identifiable in this way. Space 
and time are not peculiarly privileged universals. Like all other 
universals, they appear only as individualized; and spatial and 
temporal predicates have no more claim to define the individual- 
ity of a “this” with which they appear than do other predi- 
cates. 


1V 


To solve the antinomy of the determination of the individual 
by the universal, Leibniz makes use of the postulate of “the 
identity of indiscernibles”’: no individual can share all its pred- 
icates and relations with another, that is, only that which is dis- 
tinguishable by predicates is distinct. But this postulate takes 
advantage of the weakness of our powers of knowledge; it may 
be that we fail to make distinctions where distinctions exist. 


72 SYMBOLISM AND TRUTH 


The postulate needs to be reénforced by another, “the principle 
of sufficient reason,” from which it follows. This principle as- 
serts that everything has a reason, and since reasons are univer- 
sal, that everything (including the individual) is describable in 
universal terms. Thus the individual is connected logically, 
deductively, with the universal. 

But if an individual is determined by its predicates, so that no 
individuals can have all their characters and relations in com- 
mon, the process of distinguishing characters and relations in 
individuals should sometime come to an end. The “specific es- 
sence”’ of an individual should sometime be reached, unless it 
takes an infinity of universals to determine an individual. Faced 
with the apparently endless exfoliation of the “‘what”’ from the 
‘this,’ Leibniz added that the number of universals which de- 
termines an individual is infinite; and this leaves finite knowl- 
edge no better off, so far as the determination of individuals 
by universals is concerned, than if the individual were not so 
determined. 

If the assumption of the identity of indiscernibles is true for 
reality, it is nevertheless useless for finite knowledge. The dis- 
tinction between the universal and the individual persists in its 
original form for perception and thought. The metaphysical pos- 
tulate leaves the epistemological difficulty as it was. 


V; 


It is possible for knowledge to proceed — and it does as a 
matter of fact proceed — without answering the question as to 
whether the individual is describable in terms of universals. The 
assumption of determinism (or indeterminism), even in this 
most abstract form, is not essential to thought. 

It may or may not be true that a sufficient number of predi- 
cates determines the unique “this” of an object; the individual 
can still be thought of, it can still be referred to through sym- 





UNIVERSALS AND INDIVIDUALS 73 


bols. The individual appears in conceptual knowledge as an 2, 
as something represented by a variable symbol which we as- 
sume to have a meaning, though what this meaning is we can- 
not say. We cannot even assert that this x might not stand for 
an aggregation of universals, for it is always possible that Leib- 
niz’s infinity of predicates might be its value. But if we could not 
employ variables, which are symbols whose meaning is undeter- 
mined, we could not bring the individual into thought.! Thus 
knowledge of the individual always takes the form (xR), where 
x is a variable term and R is a quality of that term, or the form 
(xy . . . S), where z, y, etc. are variable terms and S is a rela- 
tion between them. (S or R might also be a mathematical or log- 
ical operation.) If one asks what it is to which the relation or 
quality attaches, he is driven to descriptions in terms of other 
qualities and relations; the term is lost behind essences which 
are of it but which are never it. In short, the value of the varia- 
ble continues undetermined. 

The representation of an individual through a variable elimi- 
nates a possible confusion between the individuality of a thing 
and its reality or existence; it makes clear the point that individ- 
uality may be purely conceptual. If the “this” of an object — 
the ultimate subject of all its predicates or the final term of all 
its relations — is simply the real or the existent, the individual 
is destroyed; it is absorbed in reality. This ultimate subject or 
term is represented by a variable as distinct from other subjects 
or terms — as one ofa plurality. The x which gives individuality 
to one essence is thought of as other than the y which gives in- 
dividuality to another; the indeterminateness of the z or y is the 
counterpart in thought of the inexhaustibility of the individual. 
Thus things of the imagination, which have not been presented 
and which may or may not exist, are individualized. Witness 
the characters of one’s favorite novel who, if they live in the 


1 See below, ch. IV, sec. iv, for a general discussion of the variable. 


74 SYMBOLISM AND TRUTH 


mind, are as inaccessible to complete description as any real 
persons. 

It might be thought that a proper name stands definitely for 
an individual, that the variability which is present in the repre- 
sentation of individuals is thus eliminated. But if proper names 
are more closely examined, they are found to be subject to the 
same indeterminateness which infects all references to individ- 
uals. The name “Napoleon” or the name “Stratford-on-Avon”’ 
stands for one and only one individual, but which individual we 
can know only through description (or else as a mere “this” 
numerically diverse from a “‘that’’). Napoleon is “the conqueror 
of Europe,” “the exile of St. Helena,” “‘the defeated general of 
the Battle of Waterloo”’; Stratford-on-Avon is “the birthplace 
of Shakespeare.”’ Each is an a to which characters and relations 
attach, and the proper name no more determines what z this is 
than does the description; indeed, the meaning of the proper 
name is equivalent to the meaning of one or more of these de- 
scriptions of the individual named, and the variability present 
in the description is not absent in the name. The “this” of an 
object for which a proper name stands is as elusive as the “this” 
of any other thing.! 

Since knowledge presupposes the distinction between the uni- 
versal and the individual, and since the individual is always (for 
knowledge) something other than its predicates and relations — 
represerited in no other way than through a variable x to which 
these predicates and relations attach — knowledge presupposes 
its own indeterminateness. Leibniz’s metaphysical principles of 
“the identity of indiscernibles” and of “sufficient reason” pos- 
tulate that this indeterminateness would disappear in an infinite 
knowledge; such a knowledge could assign a value to the x which 
represents the individual. But for finite thought, only proposi- 
tions which make no reference to the individual can be free from 


1 See below, ch. IV, sec. ix, for a discussion of proper names. 





UNIVERSALS AND INDIVIDUALS 75 


this indeterminateness — only propositions which are stated in 
universal terms can have an invariable meaning. For we can 
know what we mean by a symbol which stands for a universal, 
but we can never know what we mean by a symbol which stands 
for an individual; or rather, we can know only that we mean a 
“this” which is distinct from a “that.” 


VI 


The universal is determinately known, it can be represented 
in thought by a symbol whose meaning is invariable, because it 
is presented as self-identical in different ‘“‘thises”’ and “thats,” 
in different individuals. And when change renders the identity 
of the individual ambiguous, the universal — or at least some 
universal — remains what it was. Universals are strands of 
identity which spread themselves out through time and space; 
it is of the essence of universals to be recognized as the same in 
changing and diverse instances. 

There is also a perception of the distinctness of universals, 
which is perhaps more primitive than the perception of their 
identity in different instances. Cutting across the numerical di- 
versity of individuals, when they are copresent as “this”? and 
“that,” is a second (numerical) diversity — that of qualities 
and relations. The “this” is apprehended as distinct from the 
“that” in some other respect than its individuality. It is a “this 
of the sort X”’ as distinguished from a ‘‘that of the sort Y.” And 
if there are several “‘thises” and “thats,” two or more of them 
taken together may be distinct in some other respect than in- 
dividuality from two or more others taken together. This will be 
a perceived difference of relations, ¢.g., if four circles are pre- 
sented, two including one another and two excluding one an- 
other, the inclusion and exclusion are aspects in which the 
groups of two differ. “Inclusion’’ is the “what” of one group, and 
“exclusion” the “what”’ of the other. 


76 SYMBOLISM AND TRUTH 


Such diversities of qualities and relations are numerical, no 
less than are those of individuals; the universals are “‘two”’ or 
more. But this second numerical diversity is additional to the 
first; it is a numerical diversity in numerical diversity. As with 
individuals, so with universals — they need to be copresent to 
be known as distinct. But despite the fact that the distinctness 
of universals is of the same general sort as the distinctness of in- 
dividuals, the one is not reducible to the other, for the universal 
is always merely an aspect of the individual, the “what” and 
the ‘‘this” are always held apart. If I am presented with a 
white object and a black object, the perception contains two 
numerical diversities on different levels, the diversity of “this 
object” and “‘that object” and of “blackness”? and “white- 
ness.” 

Along with this perception of differences of qualities and rela- 
tions may go that of the identity of a quality or relation in dif- 
ferent individuals. The ‘“‘this” and the “‘that” may be per- 
ceived as the same in some aspect. When two white objects and 
a black object are given together there will be, beside the 
numerical diversity of the three individuals, a diversity of two 
qualities; but a single quality will be shared by two of these 
individuals. A self-identical universal will be recognized in dif- 
ferent instances. 

Mr. G. E. Moore discards this possibility of a universal being 
an “‘identity in diversity’ because a self-identical object can be 
one and one only; and he believes, as a corollary of this, that a 
self-identical universal could not be split between several in- 
dividuals and remain self-identical. The individual ‘‘ whiteness” 
of one white object, he argues, is not identically the “white- 
ness’’ of another white object. 

The difficulty arises from a confusion of identity with in- 


1 G. E. Moore, “Identity,” in Proc. Arist. Soc. (1900-1901), p. 103; espe- 
cially pp. 1165 ff. 





| 
: 


UNIVERSALS AND INDIVIDUALS ri 


dividuality. By a self-identical “whiteness”? one does not mean 
an individual white; and if there is an individual white, this is 
not a universal but the same thing as is meant by “‘a white ob- 
ject.”’ Now a white object is obviously not identical with an- 
other white object, but the “whiteness,” as a universal, is the 
same in both cases. The fact that a universal occurs with individ- 
uals which are not identical does not rob it of its own identity. 
Since identity and individuality are not the same, a single iden- 
tity can be individualized in many different cases. Each dis- 
tinct quality or relation is something in itself; it has an identity 
which makes it what it is, and if it had none it would be a non- 
entity. But to say that a universal is an identity is not to say 
that it is an individual. 

The perception of the numerical diversity of individuals, then, 
is accompanied by a perception of the diversity or identity of 
qualities and relations in these different individuals. 

What of the perception of diverse universals in a single indi- 
vidual? Obviously, a white object can be both white and round; 
it can be included in or excluded from another object; univer- 
sals, themselves static, can be grouped about a static “‘this,”’ so 
long as no ambiguity concerning the identity of the individual is 
introduced by changes in the situation. Just as we perceive (in a 
single whole of experience) the self-same universal as qualifying 
or relating many different individuals, so we perceive the self- 
same individual as entering into many different relations and as 
qualified by many different predicates. 

But every whole of experience gives way to new wholes; 
change is of the essence of experience. 

The self-identity and distinctness of the individual slips away 
behind what seem to be its changing aspects, and the universal 
alone continues to be known as the same. The waxing and wan- 
ing of a light is always light; the approach of two moving bodies, 
always motion; the alteration of colors in the field of vision, al- 


78 SYMBOLISM AND TRUTH 


ways color; the drops of water which displace one another in the 
flowing river are always of the same chemical composition. It is 
impossible to determine whether the individual persists, but a 
changeless universal is the background of the change; and the 
identity of this universal does not become ambiguous, as does 
that of the individual. 

All perceptual distinctions, therefore, excepting an immedi- 
ately apprehended difference of the “this” of one object and the 
“that” of another, are distinctions of universals; and all per- 
ceived identities, excepting the identity of a momentary “this,” 
are identities of universals. 


VII 


What has been said so far of universals and individuals is pre- 
liminary to another point — to a further characterization of 
logical form. The idea of the structure of groups is not complete 
without the concept of a universal and of the part it plays in 
groups. From the point of view of logical form, universals and 
individuals are distinguished by their structural functions. 

A universal is an aspect of a group as a whole. It is that which 
distinguishes the group from another whose constituents, apart 
from the universal, are indistinguishable from those of the for- 
mer except by their bare numerical diversity. The group as a 
whole is an instance of this universal, which is itself an element 
in the group, but not an element codrdinate with the others. 
The universal is an element of unity, while the others are 
terms. 

Group-unity is the universal of universals, it is the “what” of 
every group; and different universals are different kinds of 
group-unities. To recognize anything as a group is to recognize 
it as a unity of a specific sort, that is, an instance of a quality, a 
relation, or an operation. 

Consider the unity of a simple qualitative fact such as “Iago 





UNIVERSALS AND INDIVIDUALS 79 


was wicked.”” Here the predicate and the subject are knit 
together. The expression does not mean “Jago” and “ wicked- 
ness”? as a mere plurality, but “ Tago-as-qualified-by-wicked- 
ness.” And if the fact were a number of terms joined by a rela- 
tion or a mathematical operation, the relation or operation 
would be attached to the terms in the same general manner as 
the quality to the thing qualified. The quality, relation, or oper- 
ation is not related to its terms, for this would involve an infinite 
series of relations; we can say only that the terms enter into the 
peculiar unity which makes them a group or a fact. The fact 
“clouds precede rain,” for example, is not made up of the ele- 
ments, clouds, rain, and the relation precedes related to one an- 
other; for if this were so, there would need to be a third relation 
which unites the second relation to the original terms and rela- 
tion, and so on. If the unity of a fact depended on the knowledge 
of such an endless series of relations, the fact would not be pre- 
sented as a whole. The unity is given immediately. A relation 
relates its terms and a quality qualifies its subject once and for 
all; and this is true of the simplest fact — of a fact, for instance, 
constituted of the meagre relation of conjunction or the mathe- 
matical operation of addition. “‘A plus B” cannot mean A and 
B and plus added together, for this would demand an infinity of 
new pluses, and the fact would remain incomplete. A plus Bisa 
new entity, something other than the entities A and B and plus; 
and it is given when the terms and the operation are given in the 
unity which makes the whole an instance of addition. 

That a quality, when it modifies a subject, is of the subject in 
the sense in which an operation or relation is of its terms, is 
borne out by our habits of speech. Relations or operations are 
predicated of their terms as qualities are predicated of their sub- 
jects. One says “‘x 1s between y and z”’ as readily as “‘x ts white”; 
x, y, and 2 as a group have betweenness as z alone has whiteness. 
Thus qualities, relations, and operations, despite their differ- 


80 SYMBOLISM AND TRUTH 


ences, are alike in their structural functions.! They can be 
distinguished from the terms they unite or the subjects they 
qualify, but at the same time they are cemented to these terms 
and subjects. 

The ability to enter with other elements in a group so that the 
plurality of members becomes a whole is characteristic of uni- 
versals; and each group contains a universal which performs 
this function in it. If a fact (a complex object) is presented, the 
determination of the group by the elements attests the presence 
of a universal. The form of a fact is a blank into which the con- 
stituents must fit, and at least one of the places in the blank is 
for a universal, while the others are for terms. And even the per- 
ception of bare numerical diversity, either of individuals or uni- 
versals, is an analysis of a whole into parts which are diverse 
from one another but have unity through the relation of diver- 
sity. 

A fact is therefore something more than a union of any ele- 
ments whatsoever; it is a union of elements so that a universal 
enters into terms or subjects. The notion of a group involves not 
only the concept of members united into a whole, but also the 
concept of an element (itself a member) which determines the 
members to be a whole. But the universal is distinct from the 
terms because it fulfills a different office in the fact; it stands 
above the terms, pervading the whole and lending to it a distinc- 


1 Operations and relations, though they are like qualities in that they unite 
with terms in the same fashion, are not qualities. From the point of view of 
form, a quality modifies only one term; it is of the form (Ra). A relation has at 
least two terms; it is of the form (Sab); and if these terms are not distinct, as 
in (Saa), the relation still has two terms, so far as the representation goes 
(though these are not distinct), but the fact has only one. Such reflexive “re- 
lations”’’ are qualities represented as relations between a term and itself. It is 
the symbolic group rather than the fact which is relational in form. Opera- 
tions, on the other hand, may appear with one or more terms. They may be of 
the form of qualities or of the form of relations. But operational groups are 
distinguished from qualitative and relational groups by the way in which they 
are used in symbolic systems; they permit uses which these others do not per- 
mit. See below, ch. VII, sec. vii, for this distinction. 





UNIVERSALS AND INDIVIDUALS 81 


tive coloring. The concept of the unity of a universal and the 
terms on which it rests must be placed with the concepts of ob- 
ject, and of identity and diversity, among our indefinables. 
The Platonic description, “participation,” as nearly charac- 
terizes this unity as any we know. If one were to revise Kant’s 
list of the categories, leaving aside the question as to whether 
they are of the object or of the mind, he would find it necessary 
to include among the presuppositions of knowledge, not only 
the notion of the identity and diversity of objects, but also that 
of the peculiar unity of groups which springs from the presence 
of a “participating”’ universal. 


VIII 


If a universal is any object which can assume the réle of ele- 
ment of unity in a group, an individual must be an object which 
can take no other part than that of a term. 

Individuals alone do not constitute facts; there are no purely 
individual facts. Through universals we describe and relate in- 
dividuals, but through individuals nothing is described or 
brought into relation. ‘‘The table,” “the chair,” “the book,” 
cannot in themselves unite into a group; by their nature they 
are capable of playing the part of terms and nothing else; and 
only when they are related or qualified in some way do they be- 
come elements in a fact. (Indeed, an individual referred to as “‘a 
table,” “a chair,”’ or “‘a book,”’ is already an x qualified by a 
predicate, and has already become an element in a fact.) “The 
table with the book on it and the chair beside it” is a fact; but 
“the table the chair the book” is no fact. Words and phrases 
that signify individuals do not, by themselves, go together to 
form significant expressions, and here again language reflects 
the structure of objects. 

Without predicates, relations, or operations to bring them 
into groups, individuals (if they are thought of) continue in iso- 


82 SYMBOLISM AND TRUTH 


lation, cut off by their individuality from other objects. Such 
isolated individuals are never known concretely; it is only by 
the most violent act of abstraction that we can conceive of 
them. 

The search for a relation between a universal and the individ- 
ual which is an instance of it results, therefore, in the discovery 
that “being an instance of”’ is not a relation. The unity of a uni- 
versal with individuals is a wholeness within which relations are 
distinguished; a relation is a species of group-unity; but this 
unity is not itself related to its terms, and the statement that it 
is “in” or “of” or “with” its terms serves only to point to it as 
an indefinable. The minimal object of knowledge is a universal 
in its instance; the universal, the individual, and their unity are 
given at once. 


IX 


The distinction between terms and elements of unity is not 
the same, however, as that between individuals and universals; 
for the terms as well as the element of unity in a fact may be uni- 
versals, as in “truth is beauty,” “dishonor is worse than death,” 
‘the course of true love never did run smooth.” 

A fact whose terms are universal is not the same kind of fact 
as one whose terms are individual. The latter is concrete; the 
former, abstract; but both are nevertheless facts. An abstract 
fact is an aspect of a concrete fact; or rather, it is an aspect of 
many such facts. But in perception, facts come to us as individ- 
ualized, and not as abstract. 

The ability of universals to fulfill a double function in groups 
— both as terms and elements of unity — divests them of the 
separateness which belongs by nature to individuals. In an ab- 
stract fact such as ‘‘dishonor is worse than death,”’ a universal 
which might qualify or relate in some instance is referred to 
apart from its qualifying or relating function, and it becomes a 
term in a new fact; but the universal remains a universal be- 


UNIVERSALS AND INDIVIDUALS 83 


cause it can appear as a qualifying or relating element, rather 
than as something qualified or related. Thus when I say “‘this 
paper is white,” I refer by the word “white” to the same object 
as that to which I refer by “whiteness” when I say “whiteness 
is the symbol of purity.” The difference is not in the identity 
of the object meant, but in its function. In the one case it is a 
term in an abstract fact; in the other, an element of unity ina 
concrete fact. 

We tend to speak of facts whose terms are individuals as 
“particular,” but the word “particular”? is misleading. Every 
object or fact is in a sense particular, for it has an identity of its 
own; it is a ““somewhat”’ distinct from other objects, and it can 
be referred to as “this” object, “this” quality or relation, 
“this” fact. Particularity in the sense of identity is found 
everywhere; not only in individuals, but in universals and in 
facts whose terms are universal. “Dishonor is worse than 
death” is a particular case of the relation “worse than,” and 
everything is a particular case of the logical character of “ob- 
jectivity.”’ If one means by the particularity of an object or fact 
simply its identity, he ought to speak of particulars of higher 
and lower orders, for the world is composed of identities of 
higher and lower orders. A fact that contains as a term some ob- 
ject that enters as an element of unity in another fact is of a 
higher order of particularity than this second fact. “Dishonor is 
worse than death” is not of the same order of particularity as 
“Judas was dishonorable”’; the latter is the kind of fact from 
which the former is abstracted. The quality which appears as a 
qualifying element in the latter is itself a subject of description 
in the former; ‘‘dishonor”’ is taken now as a substantive instead 
of as an adjective. 

In this manner, facts are overlaid, the one on the other, the 
less particular on the more particular, the terms of those of 
higher orders of abstraction being separated out from those of 


84 SYMBOLISM AND TRUTH 


lower orders of abstraction, till we reach the facts whose terms 
are the most abstract of all — the facts of logical structure. But 
any fact at any stage is particular in some sense. 

The relation between these different orders is like the Aristo- 
telian relation of matter to form. The lower orders of particulars 
are the matter of the higher orders; a fact which is particular in 
relation to one fact is general in relation to another; and the 
lowest members in the scale are those whose terms are finally 
and irreducibly particular. That is, they are facts whose terms 
are capable of being terms and nothing else — whose terms are 
individuals. These terms are like Aristotle’s prime matter; they 
are cases of universals, they have form in the Aristotelian sense, 
but there is nothing in relation to which they are form. Nothing 
is an instance of them. They are that upon which universals 
rest, but which themselves rest on nothing. 

Though the individual which is an instance of a universal is 
one with the universal in the instance, the process of abstraction 
— of separating the two for thought — has begun when the uni- 
versal is distinguished in its instance. To abstract is to disregard 
an aspect of a presented object; and since all presented objects 
are of double aspect, both universal and individual, we can dis- 


regard the latter and refer only to the former. Not only can we. 


abstract from the individuality of an object; we can also ab- 
stract from any of its more specific qualities or relations. Thus a 
green object is a colored object; when I am presented with the 
relation before, I am also presented with an asymmetrical rela- 
tion; and I can refer to the color apart from the greenness, or to 
the asymmetry apart from the beforeness. The very presentation 
of objects — for they are only presented when they are known 
both as universal and individual — is the beginning of abstrac- 
tion. 

The abstraction which begins in distinguishing a universal in 
a perceived instance is completed in the realm of conception; 


~~ 


UNIVERSALS AND INDIVIDUALS 85 


the instruments of conception (symbols) are also the instru- 
ments of complete abstraction. In perception the sense of the 
oneness of the object — as an individual in which many univer- 
sals join — cannot be shut out; but through symbols any of 
these universals, or for that matter, the individual, can be re- 
ferred to alone. We can abstract the individual, as an indeter- 
minate x, from the universal, or the universal from the individ- 
ual. The abstracted universal is not referred to as it occurs in 
any special one or in all of its instances; it is meant apart from 
instances, as an object with an identity of its own. 

Needless to say, the symbol which carries an abstract refer- 
ence is not itself abstract; it is a presented object with its own 
individuality and general nature. And yet the once heated con- 
troversy over “abstract ideas” turned on a confusion between 
the abstractness of the symbol and the abstractness of its refer- 
ence. It is indeed absurd to hold, as Berkeley accuses Locke of 
holding, that ideas as images (as psychical events) are ab- 
stract; they are obviously as concrete as any other presented 
objects. But there is no absurdity in their having an abstract 
meaning. The problem of abstraction, so far as it touches uni- 
versals, comes in the end to this: Can we refer to universals as 
single, self-identical objects distinct from individuals? And this 
is the problem of the objectivity of universals. 


X 


There is no reason to suppose that a universal is any the less 
an object than the subject it qualifies or the terms it relates. If I 
say that “the afternoon is warm,” or that “Chicago is between 
New York and San Francisco,” the warmth is as objective as the 
afternoon, and the relation between as genuine a constituent of 
the fact as Chicago, New York, or San Francisco. Unless the 
concept of an object is taken in a much narrower sense than we 
have given it, universals cannot be distinguished from individ- 


86 SYMBOLISM AND TRUTH 


ual subjects and terms on the ground that the latter are objects 
while the former are not. Both are in knowledge; both are given 
as constituents of facts, though neither is given alone. 

When it is said that universals are not objective, what is 
meant is that they are not in reality the same kind of object as 
their terms when these are individuals; universals do not belong 
in the same metaphysical category as individuals. The nominal- 
ist views the world as being really a collection of individuals; 
what are called universals are to him ideas, mental addenda, 
created by an act of comparing individuals. He believes that 
white objects exist, but that whiteness does not exist — at least 
that whiteness exists only in a mind. It is a name for a number 
of things which are closely alike, that is, for an artificial con- 
struction, “‘the class of white objects.” 

In answer to the nominalist, it must first be observed that the 
question as to whether a universal exists in a mind or in reality 
(assuming that reality and “‘a mind” are different), is a meta- 
physical and not an epistemological question. Universals are 
known in some manner, whether it be as elements in an external 
or an internal world. They appear in the simplest units of cogni- 
tion; and whether or not they are contributed by the perceiving 
subject, they are objects of knowledge in the broadest sense of 
the term. For the purposes of the positive theory of knowledge, 
this is enough. We need not ask if reality is a concourse of indi- 
viduals, or if it is a network of universals without individuals, or 
if it is a fusion of both. 

There are, however, many considerations that cast doubt on 
a metaphysics which affirms that individuals are real and that 
universals are unreal. First among these is the indeterminate- 
ness of our knowledge of the individual. If the x which is quali- 
fied or related by universals is the sole known reality, knowl- 
edge touches reality only at the tiniest point — only through 
the fleeting “this” of perception, which can be described in no 


UNIVERSALS AND INDIVIDUALS 87 


way. Secondly, it appears beyond question that when one per- 
ceives a colored object he is presented with the color as well as 
the colored object. Color is given in the field of vision, and the 
fact that it might be found elsewhere is no evidence that it is not 
here. 

The nominalist will doubtless reply to this by asking how one 
can perceive an abstraction. The answer is that the color of an 
object is no more an abstraction than its individuality; the 
“what”? of an object is no less of the object than its “this.” The 
very act of perception is the beginning of abstraction; for a pre- 
sented object is both broken in two for thought (that is, ab- 
stract) and knit into a unity for perception (that is, concrete). 

Thirdly, to say as the nominalist does that an object belongs 
to a class is to notice its similarity to another object, and al- 
though the discovery of the qualities or the relations of the ob- 
ject comes through comparison, the result of the comparison is 
the perception of the universal in the object, that is, as an ele- 
ment of the whole. And if objects are similar, this similarity is a 
universal; the likeness of objects, no matter how remote, rests 
therefore on a universal. In order that the nominalist may main- 
tain his point that classification is artificial, he must either be- 
lieve that it is wholly a matter of caprice (and then it is not 
classification), or that there is some basis for it; and unless he 
wishes to negate his own view, he must show in the latter case 
that classification rests on something other than universals. 
This he does not show. 

It can be further urged, in favor of the equal right to reality of 
the universal, that objects which are known as bare identities, 
as mere “‘thises” and “thats,” still have the property of being 
objects. The very entrance of a thing on the stage of thought im- 
plies that it has a minimum of characters and relations — that 
it is identical with itself and diverse from other things. The con- 
cept of the individual itself gives rise to a universal — individu- 


88 SYMBOLISM AND TRUTH 


ality. Therefore, if universals are unreal, it ought to be added 
that all objects of thought, including individuals, are unreal; 
and the distinction between the reality of universals and in- 
dividuals falls to the ground. 

The nominalist will then ask, granting that one is presented 
with whiteness, hardness, and other sensory qualities, is one 
also presented with relations and operations? These seem to be 
much less “presentable” than qualities. But if the whole con- 
tent of the perception were a, b, c, when a is perceived to be be- 
tween b and c, this mere plurality would not be a perceived fact. 
Some sort of unity pervades and characterizes the whole; in this 
case, the relation “‘between.” But perhaps it is less difficult to 
understand how one can perceive a specific relation than how he 
can perceive this general unity. Is there a perception of the 
unity of objects? The only answer to this is that every percep- 
tion is one of the unity of objects; without a presentation of 
unity, which is not unlike Kant’s “unity of the manifold,”’ there 
is no presentation of objects. One is no more aware of objects as 
dis-unified than he is of a white object without its whiteness. 
The two cases are exactly parallel. They are cases of the appre- 
hension of the universal in its union with the individual. 

As for operations, such as (2 + 2) — they also are kinds of 
group-unity. If two objects are before me, ““twoness”’ is before 
me; and when I perceive four objects as a group of “two and 
two,” I am presented with something which approximates to a 
case of the operation plus. 

It is quite as accurate to describe the growth of knowledge by 
pointing out that the individual is abstracted from the univer- 
sal, as it is to describe it as an abstraction of the universal from 
the individual. Knowledge of the individual is not prior to 
knowledge of the universal; to discover the individual requires 
an effort of thought. And if universals are “‘ideal,”’ if they enter 
knowledge only through the working of the mind in sifting ex- 





UNIVERSALS AND INDIVIDUALS 89 


perience, the same is true of individuals. As a matter of fact, 
neither of these descriptions is true. The “this” and the “‘ what”’ 
blend in the pure awareness which underlies and completes clear 
cognition; they emerge as distinct in the perception of objects, 
but the one does not thereby become less objective than the 
other. 

To hold, with M. Bergson and Mr. Bradley, that neither qual- 
ities or relations, or the individual things qualified or related, 
are real — that all are “‘ideal’’ — is to gain at least the merit of 
consistency. Nothing short of this will do if one sets out to at- 
tack the reality of universals. But it is not necessary to prove 
that universals or individuals, or both, are real in order to vindi- 
cate their objectivity. If either, or both, are appearances, they 
are still objects; for an appearance is an object. 

General propositions, laws, and principles which ignore the 
individual have a meaning that is as much a part of the world 
of fact as the meaning of propositions whose terms are bare 
particulars. Abstraction is possible because universals are self- 
identical objects which can be singled out and referred to 
through symbols. 

XI 


The analysis of facts into terms and unifying universals is the 
basis of a general “grammar” of symbolism. Substantive sym- 
bols (symbols of terms) cannot be taken together to form signif- 
icant wholes; they must be grouped with adjectival symbols — 
with symbols of unity. Nor can adjectival symbols alone make 
up significant expressions; some of the symbols of a group must 
signify terms, whether these be universal or individual terms. 
An expression without a symbol of unity, or without terms, 
would violate a fundamental principle of the structure of fact, 
and could not possibly have a meaning among facts. 

This grammar of symbolism is the source of all special gram- 
mars. Every language, if it contains no other distinctions of 


90 SYMBOLISM AND TRUTH 


function among its words, will differentiate substantives from 
adjectives — “‘adjective”’ being taken to include all modifying 
or connecting words, that is, adverbs, verbs, conjunctions, etc., 
as well as adjectives proper. Substantives or adjectives alone will 
not, in any language, enter into significant unions with one an- 
other. Thus “‘chair table book,” “large brown on,” are intrinsi- 
cally without meaning, for they do not conform to the first prin- 
ciple of symbolic grammar. On the other hand, “book on table” 
or “large brown chair” are significant phrases (whether or not 
they stand for objects) because they are properly constructed. 
Language recognizes not only the distinction between terms and 
elements of unity, substantives and adjectives, but it recognizes 
also that the same object, if it is a universal, can play the part of 
both. A root-word assumes a different form when it enters as a 
term from the form it assumes as an element of unity. This is 
the difference between the words “‘nearness” and “‘near,”’ 
“beauty” and “beautiful,” “run” and “‘running.” These dis- 
tinct forms of words signify the same object, but they represent 
this object in different structural relations to other objects, that 
is, in its adjectival and its substantive functions. 

The signs of addition, multiplication, subtraction, and divi- 
sion are the “adjectives” — the symbols of unity — in arith- 
metic and algebra; the signs for numbers cannot by themselves 
constitute significant arithmetical or algebraic expressions. They 
must be joined by operational symbols, for an arithmetical or 
algebraic fact is made up of numbers operated on in some way. 
And a similar “‘grammar” is present in symbolic logic. (p-q) or 
(p vq) is a group in which the dot, in the one case, or the sign 
(v), in the other, stands for the unifying element, while the let- 
ters stand for the terms — for propositions united by the rela- 
tion “‘and” or “‘or.”’ 

There are many special rules for the construction of signifi- 
cant symbolic groups, but the general rule — that symbols for 


UNIVERSALS AND INDIVIDUALS 91 


terms must be grouped with symbols of unity and that symbols 
for terms or symbols of unity alone cannot have meaning, if 
they are grouped — lies beneath all systems of symbols. Any 
possible symbolic group in any possible system must follow this 
principle, since any possible fact will be a unity of terms and 
qualifying or relating universals; the most general rule of sym- 
bolic syntax rests on a “‘syntax”’ of fact — on the most general 
way in which objects fit together to form wholes. 


XII 


Each symbolic system will have its own special plan of syn- 
tax; and this plan, if it assumes no very large proportions, can 
be set forth merely by enumerating the significant groups per- 
mitted in the system. There may be no special rules for con- 
structing the groups, though none of the groups can violate the 
general principle which has just been stated. More extended and 
useful systems, such as language and arithmetic, are built on 
syntactical plans which can be embodied in rules. These rules 
state how the symbols can be taken together as significant 
wholes and how groups can be derived from one another. 

Once the syntactical plan of a system is given as a set of rules, 
expressions of many different forms can be constructed within 
it, and none of these expressions will be without syntactical 
meaning so long as it conforms to the plan. The significance of 
the groups will be a function of the meanings of their elements 
and of their form; it is necessary only that the elementary sym- 
bols of the system should stand for existing objects; the groups 
may or may not represent existing objects. 

Some systems, notably languages, contain an endless number 
of groups which fulfill the conditions of syntactical significance 
but stand for no objects. These systems are non-deductive (or 
incompletely inferential). If we follow their syntactical rules, we 
are as apt to be led away from fact (and truth) as to be led to 


92 SYMBOLISM AND TRUTH 


fact (and truth). In these systems, there is a discrepancy be- 
tween significance and truth. But in a deductive system which 
is completely interpreted there is no such discrepancy. Any 
group that can be properly derived from the original groups by 
the rules of syntax will stand for an object, that is, it will be true 
as well as significant. The conditions of significance and of truth 
are the same in a completely interpreted deductive system, and 
the rules of syntax are the rules of deduction.+ 

But in any case, the syntactical plan of a symbolic system de- 
termines its range of significance. It determines not what ob- 
jects actually are represented in the system, but how the sym- 
bols can be used significantly regardless of whether they stand 
for objects. It determines an area of concepts. 

This gives us a criterion of possibility for knowledge. A “pos- 
sibility for knowledge” in the widest sense need not be a refer- 
ence to an object; it is any meaning that is conceivable. And any 
group of symbols — of words, mathematical signs, or ideas — 
which follows the rules of syntax in a system has a conceivable 
meaning; the group is a possible concept. Possibility for knowl- 
edge belongs only to concepts, and if one says that a non-exist- 
ent object is a possible object of knowledge, this is only a man- 
ner of speaking. He does not mean that there is any such object 
to have the predicate “possible”’; he means merely that a signif- 
icant concept which refers to no object can be framed. “The 
immortality of the soul’ is conceivable and therefore a possi- 
bility for knowledge; but the possibility resides not in an actual 
fact for which this expression stands, but in the fact that the ex- 
pression has meaning. Aside from this “possibility as an object 
of knowledge,”’ the test of which is conceivability, there may or 
may not be an absolute metaphysical possibility, such as that of 
Leibniz’s infinity of possible worlds. But with this we are not 
concerned. 


1 This is an anticipation of what is more fully set forth in ch. VII. 





UNIVERSALS AND INDIVIDUALS 93 


The rules of syntax in a symbolic system therefore mark the 
limits of possibility for that system. (And in completely inter- 
preted deductive systems, every possible concept is also true.) 
But what is conceivable in one system may have no counterpart 
in another. The general rule of symbolic syntax — that symbols 
of terms alone or symbols of unity alone cannot form significant 
wholes — tells us how fact in general must be conceived; it 
marks the most general limits of possible concepts. 


XIl 


The two symbolic systems whose application to fact is at once 
most sweeping and most familiar are the systems of the imagi- 
nation (of mental images) and of language. 

The habits of correct and ordered speech become the habits of 
correct and ordered thought, so that if a thing can be thought 
clearly it can be said clearly. We grow unconsciously to accept 
certain combinations of words as significant, and to reject others 
as nonsensical because they do not conform to the rules of syn- 
tax. And yet the possibilities of significant combinations in lan- 
guage are so wide that almost any chance grouping of words has 
syntactical meaning. If words are thrown together at random it 
is more than likely that a significant phrase will be achieved, for 
no phrase that follows the rules of syntax in language is without 
meaning. 

When expressions such as “the round square,” ‘the moon is 
made of green cheese,” “Socrates is a triangle,” etc., are rejected 
as meaningless, they are not strictly speaking rejected as non- 
sense, unless we have passed over the thin line that separates 
nonsense from falsity and contradiction — that divides the 
meaningless from the fantastic. It is true that there are no ob- 
jects which correspond to these expressions, yet the expressions 
are not totally without meaning. The very fact that we say “a 
round square is a geometrical contradiction,” that ‘Socrates is 


94 SYMBOLISM AND TRUTH 


a triangle” or “the moon is made of green cheese” are fantastic 
notions, shows that we grasp these expressions as concepts; 
otherwise we could attribute neither contradiction nor absurd- 
ity to them. A nonsensical expression, an utterly meaningless 
collection of symbols, could be neither false, fantastic, or con- 
tradictory. 

And yet nonsense cannot be without a semblance of sense. 
There must be vestiges of significance in the symbols, or else 
they would not be symbols but mere collections of presented ob- 
jects. In the pseudo-phrases, “large brown on ” and “chair table 
book,” for example, the elements are significant but the wholes 
are without meaning. They present the semblance of wholes but 
they conform to no rules of syntax. In direct contrast to this 
type of nonsense stand pseudo-phrases that have a seeming in- 
telligibility as wholes since they follow syntactical rules, but 
that are meaningless through the presence of meaningless ele- 
ments. The lines from Lewis Carroll’s Jabberwocky, a classic of 
nonsense, exhibit just the proper distribution of significant ele- 
ments along with meaningless elements to give the whole a 
structure: “O frabjous day! Callooh! Callay! He chortled in his 
joy.” So powerful is the sense of significance as a whole that the 
parts tend to derive meaning through their places in the whole. 

The interpretation of words — or any symbols other than 
images — usually takes the route of the imagination, and for 
this reason it has been maintained that what cannot be imag- 
ined cannot be thought, that conceivability in images is the 
only conceivability. 

The syntax of the imagination is extremely simple. Any 
images that can be held together before the mind form a signifi- 
cant group. The distinction between terms and elements of 
unity is not made explicit, though one never imagines an object 
composed of parts which are unrelated or unqualified. There are 
no signs of grouping other than the mere juxtaposition of 


UNIVERSALS AND INDIVIDUALS 95 


images, and no juxtapositions of images are excluded as mean- 
ingless, though many are fantastic and absurd. Yet some images 
refuse to go together before the mind; there are no counterparts 


99 66 


in the imagination for “a round square,” “a curved straight 
line,” etc.; the images corresponding to these words exclude one 
another’s presence. It is difficult to give any reason for this ex- 
clusion; but this fact shows that the syntax of the imagination 
has its limits, and that there are possible concepts in other sys- 
tems which cannot be translated into the imagination. 

What is fantastic or absurd, or even contradictory, is not then 
utterly nonsensical. No properly constructed symbolic expres- 
sion is void of meaning. The general grammar of symbolism 
marks out the most general limits of possibility for thought, fol- 
lowing the most general lines of the structure of objects, while 
special plans in special systems mark out narrower limits of con- 
ceptual possibility. What is an impossibility for thought in one 
set of symbols may not be an impossibility in another set. It is 
not strange, therefore, that we can “imagine” much less than 
we can mean. 


XIV 


One class of syntactical rules must be especially noticed, that 
is, the rules of order. The sentence, “Brutus killed Caesar,”’ has 
a different significance from, “‘Caesar killed Brutus,” and the 
pseudo-group, “killed Brutus Caesar,”’ has no significance. The 
spatial or temporal arrangement of the symbols enters here as a 
factor in the meaning; the order in the symbols mirrors an order 
in the fact signified. Must we then include the spatial or tem- 
poral arrangement of symbols as a feature of their logical form? 

It is less difficult to illustrate than to describe what is meant 
by the order of a group. Facts of identical constituents may be 
wholly different in order, they may be of opposite orders. The 
fact ‘A precedes B” is different and opposite in order to the 
fact ““B precedes A”’; the facts “A between B and C,” “B 


96 SYMBOLISM AND TRUTH 


between A and C,” and ‘‘C between A and B” are distinguished 
by their orders. Most active verbs and prepositions, if they enter 
in groups, give us phrases or sentences representing ordered 
facts. “Hamlet killed Polonius” does not mean the same thing 
as “‘Polonius killed Hamlet”’; ‘grace before meat”’ is something 
other than ‘“‘meat before grace.”’ 

The simplest manner of describing order is to say that all re- 
lations have a direction, and that a fact whose elements are re- 
lated in one direction is different (for some relations) from a fact 
of the same elements related by the same relation in another 
direction. And the usual manner of representing order in lan- 
guage and mathematics bears out this description. The symbols 
of speech and writing themselves have a direction in space and 
time, and it is through this that the order in the fact is signified. 
This manner of representing order is a convenient device of sym- 
bolism, but it does not analyze order; if the order in the fact is 
not spatial or temporal, it merely represents one kind of order 
by another. 

Order is something common to groups which have a direction 
in space and time and to other groups which are non-spatial and 
non-temporal, and can only metaphorically be said to have a 
“direction.” “‘Hamlet believed the ghost” is an ordered fact, 
but “believing” is not a temporal or spatial relation, though the 
order it gives to the fact is reflected by the spatial order of the 
symbols. What is the common structural feature that makes 
this reflection possible? 

An asymmetrical (or ordering) relation not only unites its 
terms, but in uniting them, distinguishes them; it lends to each 
a distinctive mark, so that the whole is not of the simple form, 
(Rab), but of the form, (R(Sa)( Qb)). The whole is a group of 
groups, and the order is the manner in which the terms are dis- 
tributed in the sub-groups. Thus (R(Sa) (Qb)) and (R(Sb) (Qa)) 


represent different orders of the same elements. There are as 


UNIVERSALS AND INDIVIDUALS 97 


many possible orders as there are possible distributions — in 
this case, only two. 

Consider, for example, any fact in which the constitutive re- 
lation is a transitive verb, ¢.g., ““A knows B.” The relation re- 
lates the terms, but at the same time distinguishes one as “‘ac- 
tive” and the other as “passive’’; and the fact is more fully 
stated as, “A, active, knows B, passive.”’ This is plainly of the 
form, (R(Sa) (Qb)), where R is the relation “knowing,” and S 
and Q, respectively, the qualities “activity” and “passivity.” 
The relation both relates and “qualifies” its terms; though this 
must not be construed to mean that the relation is reducible to 
qualities of its terms. It is always a relation; but each term, 
through being in the relation, assumes a special character — a 
character that attaches to it only when it is in the relation. Lan- 
guage generalizes this distinction of quality which an ordering 
relation imparts to its terms into the distinction of “‘subject”’ 
and “‘object.”’ Thus in “‘a before b” or “a in b,” a is the subject 
and b the object; and in apprehending the fact as ordered, we 
grasp this distinction of relational quality in the terms. It is ap- 
prehended as of the form, (before (a, subject) (b, object) ); and this 
is different from the form, (before (b, subject) (a, object)).! 

The reason why there is a “direction” from one term to an- 
other in an ordered fact is, therefore, that these terms are mem- 
bers of distinct groups; the terms are distinct not merely as 
terms, but through their places in the whole. If they take differ- 
ent places, though the constituents of the fact remain the same, 
the fact will be different. Direction in space or time is a special 
case of this general structural feature of groups. This description 
of order applies, moreover, not only to complexes of two terms, 


1 It follows from this description of order that a fact such as “A walks and 
B runs” has order; for the terms are united by a relation, and at the same time 
distinguished by predicates. The difference between this fact and ‘‘a before b” 
is not that the former is without order, but that the distinguishing predicates 
of the terms are independent of the relating relation; they are not relational 
qualities. 


98 SYMBOLISM AND TRUTH 


but to polyadic complexes of any number of terms, in which 
there is no single direction or “‘sense”’ but a number of interre- 
lated directions. The relation ‘“‘trusteeship,” for example, dis- 
tinguishes the ‘“trustor” from the “‘trustee,”’ both from the 
thing intrusted, and all three from the “beneficiary”’ of the 
trust.) This tetradic relation gives an order to its terms by mak- 
ing each a member of a distinctive group; it is of the form, 
(R (Sa) (Qb) (Lc) (Md)). But not every term in a polyadic com- 
plex need be distinguished by an order, from the other terms: each 
between b and c,” makes no distinction of order between 6 and 
c, though it distinguishes a from both. There are in this complex 
two objects and one subject; and obviously the objects are not 
distinct from one another through the relation. Its form can be 
represented as, (Ra(Sb) (Sc)), which has only three possible 
variations of order, viz., (Rb(Sa) (Sc)), (Re(Sa) (Sb)), and 
(Ra (Sb) (Se)). 

When order is seen to be a matter of grouping alone, it can be 
represented by symbols whose spatial order is irrelevant to the 
meaning — whose group relations alone are significant. (Ra(Sb) 
(Se)), which might mean “a between b and c,” can be written 
((Sb)Ra(Sc)), or ((Se) (Sb)Ra), or ((Sb) (Sc)Ra), etc.; and all 
of these different spatial arrangements will signify the same 
order of the fact. Language finds in the passive form of expres- 
sion that order can be indicated by grouping alone. “ Polonius 
was killed by Hamlet” is equivalent to “Hamlet killed Polo- 
nius’’; and here the group of the agent (or subject) ? is distin- 


1 The other distinctions of case in language, which are additional to the 
nominative and accusative (subject and object), are generalized forms of these 
distinctions of order in polyadic complexes. 

2 Expressions in the passive form show us, further, that the distinction be- 
tween subject and object as the active and passive terms, respectively, of a re- 
lation (or as the referent and relatum) does not always correspond to the dis- 
tinction between the grammatical subject and predicate of the sentence. Only 
in the active form is the subject of the relation — or relational subject — also 
the grammatical subject; e.g., in “Hamlet killed Polonius,” ‘‘ Hamlet” is both 
the relational and grammatical subject, while in “‘Polonius was killed by 
Hamlet,” “Polonius” is the relational object but the grammatical subject. 


UNIVERSALS AND INDIVIDUALS 99 


guished by the preposition “by.” The expression has the form, 
(Polonius killed (by Hamlet)), that is, (Ra(Sb)), where R is the 
relation “killing” and S the preposition “‘ by’ — the mark of the 
agent. (Rb(Sa)) would be the alternative order. It is clear that 
in the passive form the spatial order of the words does not affect 
the significance, so long as the integrity of the groups is pre- 
served. The sentence might read, “By Hamlet Polonius was 
killed,” or “Polonius was by Hamlet killed,” or ‘‘By Hamlet was 
Polonius killed,” or even “Killed was Polonius by Hamlet.’’ In 
any of these spatial arrangements, the meaning will be the same; 
and a different order can be signified only by interchanging the 
terms in the groups. 

It is therefore only accidental, and not essential — though it 
is a useful accident — that the spatial or temporal order of sym- 
bols should be significant. 

XV 


If an asymmetrical (or ordered) fact is one in which the terms 
are distinguished by being members of different subordinate 
groups within the whole, a symmetrical fact is one in which 
there is no such distinction of terms through their membership 
in subordinate groups. Consider “A with B.” The relation 
“with” imparts no distinctive qualities to its terms; each term 
is with the other and nothing more. The fact has the form (Rab) 
and could be symbolized by this group where the spatial and 
temporal orders of FR, a, and 6 are irrelevant to the meaning. 
There are no subordinate groups here in which the terms could 
be differently distributed. 

We are in the habit, however, of representing symmetrical 
facts as if they had an order. Since the spatial order of words and 
mathematical signs is usually significant, we assume that ‘‘ A 
with B”’ means something other than “B with A” until the 
contrary is asserted. For this reason, the symmetry of such ex- 
pressions as “‘ A with B” or “a X b” is commonly described by 


100 SYMBOLISM AND TRUTH 


saying that alternative orders of the symbols have the same 
meaning, that is, that ““A with B”’ is equivalent to ‘‘B with A,” 
that “a X 6” is equivalent to “b X a.” But this is necessary 
only because the fact, which is without order, is represented by 
symbols with an order. If the fact were originally represented 
by a group such as (Rab), in which the order of the symbols is 
irrelevant, its symmetry would be apparent. Therefore, the 
commutative law in algebra and logic — that (aRb) = (bRa)— 
says nothing more than that the spatial order of the symbols is 
irrelevant to their meaning. 

The distinction between subject and object (and between 
agent and patient) is also carried over to expressions which 
stand for symmetrical facts; they are represented as if such a 
distinction were present in them. Thus “‘a is accompanied by b” 
states a symmetrical fact in asymmetrical form; but it is the 
same fact as “‘b is accompanied by a,” and to recognize this is to 
see that no distinction of subject and object (of agent and pa- 
tient) exists in the fact. The order, which is in this case a certain 
grouping of the symbols (rather than a spatial order), belongs 
only to the symbols; the fact is without order. 

Mr. Bertrand Russell describes all relations as having “sense” 
or direction; no relation, he says, is without a referent and a re- 
latum.1 This is certainly true for asymmetrical relations; the re- 
ferent and relatum are what language recognizes as the subject 
and object. But the assumption that all relations — symmetri- 
cal and asymmetrical — differentiate their terms as referent and 
relatum has no foundation in the data of perception. It rests only 
on the custom of representing all relational complexes by sym- 
bols with an order; and it obscures the true nature of symmetri- 
cal relations, for it makes them a special case of asymmetrical 
ones. The mere fact that a and b are related does not distin- 


1 See B. Russell, The Principles of Mathematics (1903), ch. 9; also, A. N. 
Whitehead and B. Russell, Principia Mathematica (1910), i, 34. 


UNIVERSALS AND INDIVIDUALS 101 


guish 6 from a in any way. Why we should say that a is the rela- 
tum any more than 6, or b the referent any more than a, is impos- 
sible to see. A relation is a kind of unity of two terms (or more), 
and only some relations distinguish, as well as relate, their 
terms. If it is assumed that all relations have *“sense,”’ it is of 
course impossible to define a symmetrical relation in any other 
way than as one which is identical in both of its senses; and this 
amounts to saying that the distinction of sense (for this sort of 
relation) is merely symbolic. The more direct way is to represent 
the fact in the first place by symbols in which there is no distinc- 
tion of sense, for this makes it clear that symmetrical relations 
are of a different genus from asymmetrical ones. 


XVI 


The representation of order in a fact through the spatial and 
temporal order of symbols is open to an ambiguity which is not 
present when the order is reproduced by the grouping of the 
symbols. ‘There is no mistaking the meaning of “A is preceded 
by B” or of “Romeo was loved by Juliet.” One knows that the 
first of these expressions means the order in which B is the re- 
ferent and A, the relatum; and that the second means the order 
in which Juliet is the agent and Romeo is the patient. But the 
expressions, “‘B precedes A” and “Juliet loved Romeo,” lack 
this explicitness of meaning; and if we could express the order of 
the fact in no other way than the latter, we should not know 
which of the alternative orders was meant. 

The symbols permit two possible spatial arrangements — 
(aRb) and (bRa) — and the fact, two possible orders; but the 
question remains, which represents which? The meaning of 
these groups must therefore be further defined. 

It is understood that “‘B precedes A” has the same meaning 
as “A is preceded by B;” that “Juliet loved Romeo” has the 
same meaning as “Romeo was loved by Juliet.” Thus a unique 


102 “SYMBOLISM AND TRUTH 


correlation is established, so that one spatial order of the sym- 
bols means one order of the fact, while the other means the al- 
ternative order. Without this further definition of the meaning, 
we should know that “Juliet loved Romeo” stands for a fact 
composed of Juliet, loved, and Romeo, taken in one of two possi- 
ble orders — taken in the order opposite to that of the fact 
meant by “‘Romeo loved Juliet.’’ But neither order of the sym- 
bols could be attached uniquely to either order of the fact. 

A complete and unambiguous interpretation of the meaning 
of symbolic expressions requires that the spatial and temporal 
order of symbols be supplemented, as a means of representing 
order, by the more accurate and general kind of representation 
through grouping. (This appears in language as the syntactical 
rule that the relational subject of a phrase or sentence precedes 
the relational object, excepting where the subject and object 
are represented by case endings, or where the sentence is in the 
passive form.) 

Order then is not an independent factor of logical form which 
refuses to be assimilated to group structure. The distribution of 
terms in distinct major or minor groups which make up a whole 
is their order. A symmetrical relation is one that groups its 
terms without distinguishing any of them through their mem- 
bership in sub-groups; and an asymmetrical relation is one that 
groups its terms so that some of them are distinct not only as 
terms, but through their membership in sub-groups. The form, 
(Rabed), is a symmetrical form (the spatial order of the letters 
being irrelevant), and can be written indifferently, (abcRd) or 
(aRbcd), etc. Similarly, the form, ((Sa)R(Sb)) is a symmetrical 
form, and can be written indifferently ((Sb) (Sa)R), ((Sa) (Sb) R), 
etc. On the other hand, (R(Sa) (Qb)) is an asymmetrical form, 
and permits the alternative order, (R(Sb) (Qa)), though it can 
be written indifferently ((Sa)R(Qb)) or ((Sa) (Qb)R), ete., in 
the one order, and ((Sb)R(Qa)) or ((Sb) (Qa)R), ete., in the 


a 


UNIVERSALS AND INDIVIDUALS 103 


other order. Only the simpler types of symmetry and asym- 
metry have been illustrated, that is, those which arise through 
dyadic and triadic relations; but the same principles for dis- 
tinctions of order hold in facts of any degree of complexity. 


XVII 


The distinction between the terms and elements of unity in 
groups raises the question as to whether a symbolic group may 
contain more than one symbol of unity and a fact more than one 
unifying element. Is every unifying element the center of a 
single group? 

In cases where simplicity of statement is desired, each group 
is viewed as if it were constituted by a single relation, operation, 
or quality. This group may enter as a term in other groups, or 
may contain terms which are themselves groups, but each group 
— whatever its part in the whole may be — will be constituted 
by one and only one unifying universal. In the arithmetical 
expression (2+ 3) X ((4+ 5) — 6), for example, there are 
several different groups, each with a single element of unity. 
The groups are piled upon one another, and none contains more 
than a single operation. But it is not necessary that only a single 
element of unity should appear in a group. 

A number of qualities, relations, or operations may act to- 
gether as unifying universals in the same group. Language 
affords many examples of expressions of this nature. If I say, 
“he is poor but proud,” I attribute to the subject, not a single 
quality, but a complex of qualities — “poor but proud.” In the 
fact, “Boston is near to and north of New York,” the terms are 
joined, not by a single relation, but by two relations. 

The elements of unity in these facts are complex. They are 
themselves groups of universals united by universals; they are 
elements of unity which themselves contain secondary elements 
of unity. “Poor but proud” has the réle of a single quality and 


104 SYMBOLISM AND TRUTH 


“near to and north of” the réle of a single relation. The facts in 
which they enter are of the forms, (Q@Ra) and (VMbc), where 
® and VY represent the secondary elements of unity. Adverbs and 
adverbial expressions always modify elements of unity — quali- 
ties, relations, connectives — and give rise to complex elements 
of unity. When the forms of symbolic expressions and facts are 
described, the complexity of the elements of unity cannot be 
neglected if the description is to be complete; for this is a gen- 
uine aspect of their form. However, for purposes of simplifica- 
tion, a complex element of unity can be treated as a single uni- 
versal; and if this assumption is made, the form (Q®@Ra) is the 
same as (Na), and the form (7 VMbc) the same as (Kbc). But it 
must not be forgotten that this is an artificial simplification of 
the structure, and that a full description of the form would not 
overlook the complexity of the element of unity. 


XVIII 


The present chapter, beginning with the distinction between 
universals and individuals, has examined the function of univer- 
sals as elements of unity in facts, and has shown how this func- 
tion is mirrored by symbols which perform a corresponding 
function in symbolic groups. 

The individual and the universal are present in all concrete 
wholes of knowledge, for there is no presented object which is 
not at once a unique “this” and a “this” with some characters 
and relations. For finite knowledge, these characters and rela- 


1 The multiplicity of a group, it has been said, is determined by the number 
of its constituents, that is, the number of its terms plus one; for the element of 
unity (which, if it is complex, is treated as a single entity) is a constituent 
though not a term in the group. But in classifying relations as monadic, dyadic, 
triadic, etc., account is taken only of the number of terms they unite, and 
thus, according to our definition of multiplicity, a dyadic relation would cou- 
stitute a triadic group, etc. This is merely a matter of terminology; the multi- 
plicity of a group could be defined by the number of its major terms rather than 
its major constituents, so that a triadic relation would constitute a triadic 
group, etc. 


UNIVERSALS AND INDIVIDUALS 105 


tions do not determine the individual; and in this respect spatial 
and temporal relations are no exception, for the concepts of 
space and time are built on the perception of the numerical 
identity and diversity of individuals, and individuals are lo- 
cated in space and time only by reference to other individuals. 
Though it is possible to assume, with Leibniz, that an infinity of 
universals would determine an individual, this assumption is of 
no aid to finite knowledge. The distinction between the “what” 
and the “this” continues in its original form. The individual, 
however, is brought into conception through the use of a varia- 
ble symbol, to which no value is assigned; but this is the only 
way in which the individual as such can be thought. Knowledge, 
in referring to the individual through a symbol of indeterminate 
meaning, presupposes its own indeterminateness. 

The universal, on the other hand, is presented as an identity 
in diverse individuals — in changing and different instances. 
A changeless universal persists in the background of every 
change. Therefore the universal can be represented by symbols 
cf fixed meaning, and knowledge in universal terms, that is, law, 
is freed from the variability which infects all knowledge of the 
individual. 

Universals fill a unique réle in groups. They are elements of 
unity and themselves members of the group, but not members 
codrdinate with the others, which are terms. A relation, a 
quality, or an operation is not related to its terms; it is one with 
them, and at the same time distinguishable from them. The 
unity of a group is its “‘ what,” different universals are different 
kinds of group-unity, and there is no group which is not such a 
unity; the concept of group-unity is an indefinable but essential 
part of the concept of a group. 

Individuals play the part only of terms; without universals 
they do not enter into wholes; no fact is constituted solely by 
individuals. But the terms of a fact, as well as its element of 


106 SYMBOLISM AND TRUTH 


unity may be universal, in which case the fact will be abstract. 
Abstract facts are aspects of concrete facts, that is, of facts whose 
terms are individual; they are separated out from the individ- 
ualized data of perception. This separation begins in the per- 
ception of a universal in its instance, and is completed in the 
realm of conception by the use of symbols which ignore the in- 
dividual and refer only to the universal apart from any or all in- 
stances. The problem of abstraction — whether universals can 
be thought apart from individual instances — is the problem of 
the objectivity of universals; for if universals are objects, they 
can be referred to through symbols as single and self-identical 
things. Nominalism, by attacking the reality of universals, does 
not disprove their objectivity; if universals are “appearances” 
or mentally constructed elements in knowledge, they are still ob- 
jects of knowledge, for such appearances (or mental constructs) 
are objects of knowledge. 

A general “grammar” of symbolism rests on the distinction 
between terms and elements of unity. Symbols of terms alone 
(substantives), or symbols of unity alone (adjectives), cannot 
constitute significant expressions; and this fact is recognized in 
all symbolic systems — in language, in mathematics, in logic. 
Possibility for knowledge is conceivability in a symbolic system; 
and any possible object of knowledge must be composed both of 
terms, which may be individual or universal, and of unifying 
universals. Special plans of syntax mark the limits of conceiva- 
bility, of possibility, for special systems, and what is possible in 
one system may have no counterpart in another. Thus no ex- 
pression that follows the rules of syntax in a system is nonsense, 
though its meaning may be fantastic or contradictory, and a 
possible concept may or may not refer to an actual object. 

Rules of order are a special class of rules of syntax. The spatial 
and temporal order of the symbols is significant in most sys- 
tems; it reflects an order in the fact. But order can be described 





UNIVERSALS AND INDIVIDUALS 107 


and represented through group structure alone, since an order- 
ing relation (or operation) is one that both unites and distin- 
guishes its terms, this distinction arising through the member- 
ship of the terms in different sub-groups within the whole. 
Order must be represented through group structure if all am- 
biguity of interpretation is to be eliminated. 

Finally, the elements of unity in groups may themselves be 
complex; they may be groups composed of universals united by 
a secondary element of unity. 

The study of grouping, of the manner in which elements de- 
termine wholes, both in the fact and in the symbols, is necessary 
to the understanding of any expression. It is here that nuances 
of meaning are hidden. Sentences made up of many qualifying 
adverbs, adjectives, phrases, and clauses are susceptible of 
subtle shades of interpretation, or misinterpretation, according 
as they are taken in one or another of several possible groupings. 
The group structure, the form, is presented in the symbols and is 
immediately apprehended in its entirety, as is a musical phrase 
or a visual design. No description of the intellectual processes is 
better than Plato’s — “the contemplation of forms”’; for forms 
do not arise without universals, and they are themselves uni- 
versals, present in thought, through which the mind fastens on 
its objects. 


CHAPTER IV 


DESCRIPTION AND ANALYSIS 


I 


Tere are two ways of referring to objects —by single 
words or symbols and by descriptions. A description is a phrase 
such as “the bard of Avon,” “‘an enemy of the people,” “some 
member of Parliament,” “the divine right of kings.”’ The de- 
scription may be either ambiguously or unambiguously inter- 
preted, and it may refer either to an individual or a universal. 
In any case, it signifies an object through some of the predicates 
(relations or qualities) of the object, and it is a different form of 
reference from a single symbol, which might mean the same 
object. 

Mr. Bertrand Russell, who has thoroughly analyzed the na- 
ture of descriptions, believes that a description has meaning 
only in use; that it is an incomplete symbol which, apart from 
some proposition in which it occurs, is meaningless; ! while on 
the contrary he believes that single words and proper names are 
complete symbols; they have significance in their own right, 
either in or out of a context. Mr. Russell’s theory of descrip- 
tions rests on a conception of meaning wholly different from the 
one developed here. It can be shown that descriptions have syn- 
tactical meaning, whether or not there is an object for which 


1 In the Principia Mathematica of Messrs. Whitehead and Russell, how- 
ever, the term “descriptive phrase” is used to cover only expressions pre- 
ceded by “‘the’’; it is merely these expressions which are said to be incomplete 
symbols, 7. e., to have meaning only in use. For the purposes of unifying and 
simplifying the present discussion, we shall speak of all phrases preceded by 
the particles “‘the,” “‘a,” “any,” “some,” “‘all,” “‘each,” and “every,” as 
descriptive phrases. But it must be remembered that what Mr. Russell says 
of descriptive phrases, in the Principia Mathematica at any rate, applies only 
to expressions preceded by “the.” 





DESCRIPTION AND ANALYSIS 109 


they stand, and that their significance does not depend on their 
context. 

In The Principles of Mathematics, Mr. Russell deals with de- 
scriptions under the head of denoting phrases. ‘‘The notion of 
denoting,” he says, “like most notions of logic, has been ob- 
scured hitherto by an undue admixture of psychology. There is 
a sense in which we denote, when we point or describe, or employ 
words as symbols for concepts; this, however, is not the sense 
that I wish to discuss. But the fact that description is possible — 
that we are able, by the employment of concepts, to designate a 
thing which is not a concept — is due to a logical relation be- 
tween some concepts and some terms, in virtue of which such 
concepts inherently and logically denote such terms. It is this 
sense of denoting which is here in question. . . . A concept de- 
notes when, if it occurs in a proposition, the proposition is not 
about the concept, but about a term connected in a certain pe- 
culiar way with the concept. If I say ‘I met a man,’ the propo- 
sition is not about a man: this is a concept which does not walk 
the streets but lives in the shadowy limbo of the logic-books. 
What I met was a thing, not a concept, an actual man with a 
tailor and a bank account or a public-house and a drunken 
wife.” } 

Mr. Russell does not here explicitly take the position that the 
denoting or descriptive phrase has no meaning apart from a 
proposition in which it occurs; this is a later addition to his 
thought. But the problem he puts is the one that must first be 
faced in examining the nature of descriptions. 

The object meant by a description is a term and not a con- 
cept or mediating entity of any sort; it is a term referred to 
through universals which cluster about it. The concept means 


1 B. Russell, The Principles of Mathematics, 1903, ch. 5. In a later state- 
ment on denoting, Mr. Russell abandons the idea of a relation by which con- 
cepts inherently and logically denote terms and states his theory of descrip- 
tions without this presupposition. See, Mind, N. S., 1905, xiv, 479 ff. 


110 SYMBOLISM AND TRUTH 


the term indirectly through predicates or relations of the term, 
and it does not mean simply these predicates or relations. “‘The 
friend of Caesar” does not mean a concept, nor does it mean 
“*friendship for Caesar”; “a man”’ does not mean ‘‘manhood”’ 
or “manliness”; “‘an enemy of the people” does not mean 
“‘enmity for the people.’’ Each of these phrases means that to 
which the predicates attach; the term is signified through uni- 


versals which modify it. 


lI 


Now universals always appear in instances; they either mod- 
ify individual terms directly, or modify universal terms which 
are themselves attached to individuals; and the “relation” in 
virtue of which some concepts inherently and logically denote 
some terms is that they refer to universals which are in unity 
with these terms, so that the terms are ‘‘an instance of” these 
universals. The unity of fact is such that any predicates which 
attach, let us say, to Shakespeare are genuine aspects of this in- 
dividual, whether or not they completely exhaust his individual- 
ity. “Bard of Avon” is therefore capable of denoting the term 
with which it has this unity; “‘man” is capable of denoting any 
individual of which ‘“‘manhood” is a predicate; every reference 
to a universal or complex of universals is capable, inherently and 
logically, of becoming a reference to terms. 

A descriptive phrase rests on the knowledge of a fact in which 
the object described appears as a term. An object known to have 
such and such predicates or relations can be described as “the” 
object or “an”’ object of these predicates and relations. The 
unity of terms with their predicates makes this possible. But the 
description is not tantamount to a statement of the fact in which 
the term appears: to say that “Shakespeare wrote Romeo and 
Jultet” is not to describe Shakespeare as “the author of Romeo 
and Juliet.” The description is based on a knowledge of the fact, 





DESCRIPTION AND ANALYSIS 111 


and includes a reference to the fact, but it is something other 
than a statement of the fact. “Shakespeare wrote Romeo and 
Juliet” means that there is a certain relation between certain 
terms. “The author of Romeo and Juliet” means one of these 
terms — Shakespeare; though in meaning this person, it also 
means in some sense that this person wrote Romeo and Jultvet. 

There seems to be a reason, therefore, for distinguishing be- 
tween denoting or descriptive phrases and propositions — propo- 
sitions being references to complex wholes of terms, predicates, 
and relations, and denoting phrases being references to terms 
alone, though not without some accompanying subordinate 
reference to complex wholes in which the terms occur. In the 
traditional terminology of logic, a description denotes a term and 
connotes a proposition about this term; “the author of Romeo 
and Juliet” denotes Shakespeare and connotes Shakespeare’s 
writing of Romeo and Juliet. But this separation of connotation 
and denotation throws no light on the problem; it merely dis- 
tinguishes two sorts of meaning which, once they are admitted 
as distinct, cannot be brought together under any single concept 
of meaning. 

Mr. Russell undoubtedly has in mind some such distinction, 


> 


though he does not speak of “‘connoting,”’ when he says: “A 
concept denotes when, if it occurs in a proposition, the propo- 
sition is not about the concept, but about a term connected in a 
certain peculiar way with the concept.” Without doubt the 
proposition, “I met a man,” is not about the concept “a man” 
or about ““manhood.” It refers to a person, an individual. Nor 
is the proposition, “I have seen the portrait of the author of 
Romeo and Juliet,” a reference to some mediating entity, to 
some concept, or merely to the authorship of this play; it is 
about Shakespeare. And yet each of these propositions is about 
more than a bare term. It is about the term as it is qualified in 
a certain way, that is, as “‘an”’ instance or “the” instance of a 


112 SYMBOLISM AND TRUTH 


predicate. “I met a man” means more than “I met 2x”; it 
means “I met x and z is human.” “T have seen the portrait of 
the author of Romeo and Juliet’? means more than “I have 
seen Shakespeare’s portrait”; it means this, and “that Shake- 
speare wrote Romeo and Jultet.” If the proposition is not about 
a predicate taken in abstraction from a term, neither is it about 
a term taken in abstraction from a predicate. It means the 
predicate as it is particularized in a term. 

A descriptive phrase cannot, therefore, be distinguished from 
a proposition on the ground that a proposition means a complex 
whole while a descriptive phrase means only a single term. A 
descriptive phrase means, as any complex of symbols means, 
through the meanings of its elements, and it means a complex 
whole. It sets up a complex intention, which is a function of the 
simple intentions of its elements; and although it does not state 
the fact on which the description is based, it refers to this fact. 
It is misleading to say that a descriptive phrase denotes a term, 
and that this exhausts its meaning. The phrase means (and 
where connoting is not distinguished from denoting, it denotes) 
the predicates through which the term is described no less than 
the term; the term could not be signified through predicates un- 
less the predicates were also signified. 


III 


A descriptive phrase differs from the proposition on which it 
is based through its form. It is no less a reference to a complex 
object, to universals as they enter into unity with terms, than 
the proposition; but its form, unlike that of the proposition, is 
one in which a term — the term described — takes a central 
position, so that this term receives an emphasis it would not 
have in a different structure of the same elements. The term is 
viewed (is placed in a group) as a subject qualified by certain 
predicates — predicates which may be simple qualities such as 





DESCRIPTION AND ANALYSIS 113 


“humanity” or a complex set of relations to other terms, such 
as “‘author of the greatest tragedies in English literature.” The 
group revolves about the term. At the same time, this term is 
symbolized by a variable, which in language is presupposed 
rather than explicitly presented in the symbolism. Thus a de- 
scription is a variable reference to a particular instance of a uni- 
versal or of a complex of universals and terms. 

A particular instance of a universal is a “this of some sort”’ or 
a “this in certain relations”’; it is an object of the form (xR), 
where R is the universal (or the complex predicate) and z is a 
term. The particles which precede descriptions inform us that 
the expression is to be construed as meaning an object of this 
general structure. ‘‘ The friend of Caesar” is to be interpreted as 
standing for z as qualified by friendship-for-Caesar; “the author 
of Waverley” to mean y as qualified by authorship-of-Waverley; 
“aman” to mean z as qualified by humanity.! But the particles 
also tell us more than this; they tell us that a variable is present 
in the symbolism, and that an interpretation for this variable is 
to be chosen in a certain way. 

A descriptive phrase refers then to a fact or complex object, 
one of the constituents of which (in language) is not explicitly 
mentioned in the phrase but is understood through the use of 
the particle, and this constituent is the term — the zg, y, or z — 
described. The very omission of the term focuses the attention 
on it. Such a phrase is, in one sense at least, an incomplete sym- 


1 The central position of the term described can be indicated by writing it, 
with different typographical stress, both outside and inside the descriptive 
expression. Thus “‘the friend of Caesar,’ which means an x as modified by 
the whole complex “‘friend of Caesar,” could be written “the x ((x friend) of 
Caesar).”’ This shows that the entire expression, as well as the single predicate 
“friend,” modifies the term described. In our general schematism, this de- 
scription is of the form (x ((xJ4)Sa) ); that is, the predicate M attaches im- 
mediately to x, but at the same time z is modified by the whole complex predi- 
cate of which M is merely one element. In short, the entire structure pivots 
about x. If the complex predicate ((xM)Sa) is represented simply by R, the 
form becomes (aR). 


114 SYMBOLISM AND TRUTH 


bol, but not in Mr. Russell’s sense. It is incomplete not because 
it is meaningless outside a context, but because there is no sym- 
bolic element in it which corresponds to the term described. 
This element must be supplied in interpreting the expression; 
and it is always a variable. 

The discussion of the form of descriptive phrases leads first to 
an examination of the nature of a variable, and secondly to a 
reéxamination of the concept of the analysis of objects; for a 
descriptive phrase is analytical (and variable) in meaning, and 
in this respect it is distinguished from a proper name or a single 
symbol, which is unanalytical in meaning. 


IV 


Nothing more is known of the term described than that it is a 
term modified by certain predicates. The x or y which the par- 
ticle preceding the description permits us to supply is a symbol 
of whose meaning we are ignorant. It may stand for anything at 
all. 

“In mathematical logic,’ 


> 


says the Principia Mathematica- 
‘any symbol whose meaning is not determinate is called a vara, 
able, and the various determinations of which its meaning is 
susceptible are called values of the variable.’ It is apparent 
that a variable cannot be without meaning, for if this were the 
case it would not be a symbol; there is no such thing as a mean- 
ingless symbol. And yet, if the meaning of a symbol is unde- 
termined, does this not amount to being without a meaning? 
Apparently there is an important shade of difference between 
that which is meaningless and that which is indeterminate in 
meaning. 

The difference is this: if I know that a mark or a sound — or 
any other presented object — is to be interpreted as a symbol, 


1 Whitehead and Russell, Principia Mathematica, i, 4. 





DESCRIPTION AND ANALYSIS 115 


but do not know what interpretation is to be put on it, this mark 
or sound is a variable. The phenomenon is analogous to the sig- 
nificance present in the words of a foreign language incompletely 
understood. A sufficient number of the words are grasped to 
enable us to know vaguely what the ones that are not grasped 
mean; the latter are treated as symbols, and yet they do not 
have a determinate meaning. Our attitude toward 2, as it 
appears in the expression, “xz is human,” is exactly this: if the 
whole is to be significant, x must have a meaning. We are logi- 
cally compelled to think of x as a symbol, just as we are logically 
compelled to think of the words which are not understood in the 
foreign phrase as symbols; but though z is a symbol its meaning 
is undetermined. 

A variable is therefore indeterminate in meaning because it is 
uninterpreted. It functions as a symbol because we know — not 
through knowing its meaning, but on other grounds — that it is 
symbolic; and yet, being symbolic, it means nothing in partic- 
ular. 

Variable symbols do not arise in knowledge merely through 
the accident of ignorance; the analogy of the uninterpreted 
words in the foreign language is not perfect. Variables are in- 
troduced for a purpose. We replace the constant “Socrates” in 
**Socrates is human implies Socrates is mortal’’ by a variable 
A, and thus achieve generality of reference — “A is human im- 
plies A is mortal.” Variables are instruments of thought em- 
ployed for a definite end. But it is essential to this end that no 
specific reference, no special intention, be attached to the vari- 
able; it must continue uninterpreted; it must be used with an 
intended ignorance of its meaning. 

The circumstance which permits the introduction of variables 
is that symbolic groups have a structure and a meaning as a 
whole. A variable presupposes a context — a context of inter- 
preted symbols or a general schematism of symbolic grouping; 


116 SYMBOLISM AND TRUTH 


and thus it is the truly incomplete symbol. In this context, the 
variable, by virtue of being a part of a whole which is taken to 
be symbolic, is itself taken to be symbolic. The meaning of the 
whole tends to lend significance to the parts, which have no 
specific meanings, that is, which arouse no intentions directed 
toward objects; and this derived (variable) significance is a new 
and peculiar kind of meaning, different from syntactical mean- 
ing or from the direct reference to objects through simple sym- 
bols. Out of its context a variable is meaningless; it is not a 
symbol and not a variable. In its context it has meaning, for if 
any group of marks or sounds is construed as being significant 
as a whole, the elements must also be construed as being signifi- 
cant. This is a structural necessity. 

Take any significant group of symbols — a phrase, a mathe- 
matical or logical expression — the elements of which have a 
determinate meaning, and replace these one after another by 
elements which in themselves mean nothing. The substituted 
(and intrinsically meaningless) elements will become variables, 
and the group as a whole will continue to be significant so long 
as it is construed as a group. If in the sentence, “San Francisco 
is in California, and California is in the United States, implies 
San Francisco is in the United States,” I insert the otherwise 
meaningless marks, 2, y, and 2, for the proper names, the phrase 
becomes, “‘z is in y and y is in z implies z is in z”; and 2, y, and z 
are now variables. The phrase does not lose its meaning as a 
whole, but becomes less determinate; it becomes more general. 
But since the words “‘in,” “and,” and “implies” still have a 
fixed meaning, the statement is determinate for these, and inde- 
terminate only for x, y, and z. When all of the constituents of a 
symbolic expression are replaced by variables, the limit of inde- 
terminateness is reached. The only constant element of meaning 
that remains is the form, but so long as this form is not destroyed 
the expression continues to be significant as a whole. Its mean- 





DESCRIPTION AND ANALYSIS 117 


ing is highly general, for it is restricted to no special object, but 
only to objects which exhibit this form. 

Only the most abstract kinds of thought make use of symbolic 
groups in which all the constituents are variable and the form 
alone is constant.! But if a general schematism of grouping — a 
plan of syntax — is given, so that any group which falls within 
the plan can be treated as a significant whole, this condition 
will determine a sufficient framework for the use of variables as 
instruments of meaning. Thus ((Rab)S(Qdefg)) is a significant 
complex in which all the constituents are variables, provided the 
parentheses are taken as signs of grouping, the small letters as 
symbols of terms, and the capitals as symbols of unity. With 
these assumptions, this expression is of determinate logical 
form; but without the minimal context of a symbolic structure, 
the letters would not be variable symbols, but mere letters. 

The form of the expression in which a variable occurs there- 
fore places certain general limitations on the interpretation of 
the variable. Unless the structure is to be destroyed and the sig- 
nificance of the whole to disappear, some of the constituents 
must be interpreted as terms and others as elements of unity. 
There must be some indications in the symbolism as to which of 
the variables are to be thus construed. In “a is human implies 
x is mortal,” x must be taken as a term, or substantive; in 
“Socrates is R implies Socrates is S,’’ R and S must be con- 
strued as elements of unity, or adjectives. Universals in their 
adjectival function are not possible values of variable terms, and 
substantives (either individual or universal) are not possible 
values of variable symbols of unity.? Without this restriction, 
any interpretation would be formless and meaningless. 


1 See ch. VII for an example of such a system and for a discussion of “func- 
tional” variability, which is different from the “interpretational”’ variability 
here treated. 

2 This is the idea which lies behind Messrs. Whitehead and Russell’s 
theory of types. See Principia Mathematica, vol. i, ch. 2 of the Introduction. 


118 SYMBOLISM AND TRUTH 


Aside from this general limitation imposed by the form, the 
variable can stand for any object, or it can be given a meaning 
which is a reference to no existent object; it can be defined as 
equivalent to a symbolic group which stands for nothing. The 
x in “I saw x yesterday’ may mean “‘the prince of fairies”; the 
y in “‘y is human implies y is mortal”? may mean “the devil” or 
“the god Pan.” } 

However the variable is interpreted, it must be interpreted 
univocally; otherwise the principle of identity would be violated. 
The same symbol can have one and only one meaning; and if an 
undetermined z is construed in one way in one context, and in 
another way in another context, it is not the same symbol. In 
“x is human implies z is mortal,” the two 2’s, if they are given 
values, must be given one value. In the Principia Mathematica, 
this is stated as the special principle of “the identity of the 
variable’’; but this principle is not different from the law of 
identity in its most general form as a principle of symbolism. 
If x is the same symbol as x, whether its meaning be constant or 
variable, the two must have a single meaning. For this reason — 
that a symbol can stand only for a single (self-identical) object 
— an ambiguous expression such as “a man,” in “I met a man,” 
can mean one and only one individual if it is interpreted, but, 
being uninterpreted, it does as a matter of fact mean no indi- 
vidual. This raises the question of the ambiguity of the variable. 

1 The borrowed significance of the variable symbols in knowledge is much 
like that of the nonsense words in Lewis Carroll’s “‘O frabjous day! Callooh! 
Callay! He chortled in his joy.” And if one gives way to the inevitable drift of 
significance which is present in these nonsense verses, he finds himself treating 
“‘chortled” and “‘frabjous” as variables — as words which must have a mean- 
ing; he is left free to interpret them as he chooses, provided he remains within 
the structure of the groups. “‘Frabjous” is evidently an adjective, and “chor- 
tled”’ a verb; this is fixed by the logical form. But the charm of the verse is 


that nothing more is fixed; within these limits the words might mean anything 
whatsoever. : 








DESCRIPTION AND ANALYSIS 119 


V 


Psychological ambiguity or equivocation is the use of a word 
in several senses at once, that is, with a number of different 
intentions; and it is distinguished from the univocal use of 
words, which is their use in one sense only, that is, with a single 
intention. Clearly, logical ambiguity is not equivocation. A vari- 
able does not actually set up an intention; it actually has no 
reference until it is interpreted. It is ambiguous in the sense 
that it is susceptible of many interpretations, it can be taken to 
stand for many different objects or its value can be defined in 
many different ways, though none of these values is necessarily 
its interpretation. An equivocal symbol, on the other hand, is 
susceptible of no interpretations but the ones that already go 
with it. Each of its interpretations is a constant reference and 
some one of them must be taken, in any case, as the meaning. An 
equivocal symbol is never variable. Consider this Shakespearean 
pun: “Adam was the first that ever bore arms. The Scripture 
says, he digged: could he dig without arms?” ! “‘Arms” is not a 
variable, it is not equivalent to an 2; if it had no determinate 
meanings, there would be no pun. 

Thus a variable is ambiguous — is open to many interpreta- 
tions — for the same reason that it is a variable, that is, because 
it is actually uninterpreted. Its values are “possible interpreta- 
tions”; they are objects which might be but are not meant, or 
intentions which might be but are not aroused by it. The psy- 
chological effect of a variable, e¢.g., in “I saw x yesterday,” is to 
cause one to run over in his mind a number of meanings which 
could be attached to # and still allow the sentence to be signifi- 
cant as a whole; but the mind stops at none of these, for x does 
not mean some one of them. These meanings are possible inter- 
pretations of x; x has no actual interpretation. 


1 Hamlet, act V, scene 1. 


120 SYMBOLISM AND TRUTH 


The variable may be treated, however, as if it had only one 
possible value, and in this case it will not be a means of generali- 
zation, as it is when it has many possible values. It will be a 
variable with a constant (though undetermined) value, an un- 
ambiguous variable. And this is the difference between the 


99 66 


meaning of “the” and of “a,” “an,” “any,” and “some.” 

These particles, which precede descriptive phrases, are signs 
of interpretation. They do not signify constituents of the fact (if 
the expression stands for a fact), but they mean that a variable 
is present and that this variable is to be interpreted in a certain 
way. Each of the particles indicates a different manner of inter- 
pretation.1 

The particle “the” signifies that there is only one possible 
value of the variable. The meaning of the description, “the cen- 
ter of gravity of the solar system,” is x as modified by this com- 
plex predicate, where it is understood that there is one and only 
one possible a. But how can a variable have no more than one 
possible value and remain a variable? Does it not then become 
a constant? Clearly it does not, for the z is a variable so long as 
that single value is undetermined. If one says that “‘the center of 
gravity of the solar system is a constant,” he does not mean that 
this object is determinately (invariably) referred to; he means 
that there could be no more than one object which this descrip- 
tion signifies. (The particle “the” is sometimes used as equiva- 
lent to “‘a.”’ We say that “Brutus was the (a) friend of Caesar, 
and Anthony was the (a) friend of Caesar,’ where we do not 
mean that either was the only friend. This is a loose use of 
“the”, and it is evident that in the phrase, “the center of 
gravity of the solar system,” it is not to be construed in the 
sense of “a.” 


99 66 99 66 


The particles “a,” “an,” “any,” and “some,” on the other 


1 “Every” and “‘each”’ must be treated separately since they involve the 
idea of “‘all,”’ that is, of reference to a class. 





DESCRIPTION AND ANALYSIS 121 


hand, precede descriptions in which the variable is to be am- 
biguously construed, that is, as susceptible of many possible 
meanings; and this is the sole difference between a description 
such as “‘the bard of Avon” and “a bard of the sixteenth cen- 


39 


tury.” Both expressions are of the general form (xR), though x 
is not explicitly given in the symbolism; both refer through an 
undetermined symbol to a term as it is modified by a complex 
predicate. But the one specifies in advance that the variable has 
only one possible value, while the other specifies that it has many 
possible values. The one is an indeterminate but unambiguous 
reference, the other, an ambiguous (and therefore indetermi- 
nate) reference to a term. 

A description introduced by the particle “a” or “an” can be 
construed as if it meant either “any” or “‘some”’; but if the 
particle “any” or “some”’ is present, a further condition of in- 
terpretation is added to the general condition of ambiguity 
which is signified by “a” and ‘“‘an.”’ If I say, “‘a woman has the 
same right to education as a man,” I mean any woman and any 
man; but if I say, “I saw a woman and a man on the street 
yesterday,’ I do not mean any woman and any man; I mean 
some woman and some man. And either of these unexpressed 


ce 99 


meanings can be read into a description prefaced by “‘a”’ or 
peatits « 

The particle “any” indicates that a value chosen as the in- 
terpretation of the variable must be chosen at random from 
among the possible values; there must be no principle of selec- 
tion. Thus “any man” means “a man” where there is no rea- 
son to suppose that one of many possible interpretations is pre- 
ferred to another. ““Some man,” on the other hand, means ‘‘a 
man” where the interpretation is not chosen at random, but by 
some principle of selection not stated. “‘Some” is the antithesis 
of “any,” though both are ambiguous manners of reference, 
that is, the phrases in which they occur may have many differ- 


122 SYMBOLISM AND TRUTH 


ent values. But “some” differs from “‘any’’ in implying a specific 
condition according to which the value is to be chosen. “Any” 
implies that there is no such condition. 

If I say, “Some man is your friend,” I am speaking ambigu- 
ously. There are many possible values of “some man’’; and yet 
I do not mean that “any man is your friend,” for it is assumed 
that the choice is limited in some way. What I mean is: ““Some 
man is your friend, and not any man, because you care only for 
good men,” or “‘because your tastes in friends are not catholic,” 
etc. There is a presupposed but unexpressed condition of choice. 
And if I say, ‘“‘Not some man, but any man, is your friend,” the 
implication is exactly the opposite: that there is no condition of 
selection.! 

Whether a descriptive phrase be ambiguously or unambigu- 
ously interpreted, whether it be preceded by “the,” “a,” “any,” 
or “some,” it must, if it is assigned a meaning, be given one and 
only one meaning; it must be univocally interpreted, otherwise 
the principle of identity would be violated. And this is the para- 
dox of the variable: that, being capable of many possible deter- 
minations (excepting when it is preceded by “the”), being an 
instrument of generality of reference, it must, nevertheless, be 
given no more than a single meaning, if it is given a determinate 
meaning. . 


VI 


A term described need not be an individual. ‘‘The divine 


99 66 


right of kings,” “the royal color,” are variable (and unambigu- 


ous) references to universals; while “‘a talent for music,” “any 


33 66 


love of beauty,” “some hope of immortality,” are variable (and 
ambiguous) references to universals. 
Universals no less than individuals are instances of universals; 


1 “Some” carries no reference to existence as a necessary part of its mean- 
ing; it is not to be distinguished from “any” in this respect. “Some angel’s 
soul” does not mean that “there exists an angel’s soul.” 





DESCRIPTION AND ANALYSIS 123 


and for this reason, they can be described through their predi- 
cates and relations. A universal need not be particularized in in- 
dividuals alone; it can be particularized in other universals, 
which are in their turn particularized in individuals. The uni- 
versal described is referred to in abstraction from any or all of its 
individual instances; it becomes the value of z in the description. 
This x, being a term however, will mean the universal in its sub- 
stantive rather than in its predicative or relating form. “The 
divine right of kings” means (unambiguously) a right of a pe- 
culiar sort; “any interest of mankind’’ means (ambiguously) 
an interest of a special sort; but neither means an individual. 

A described universal is thus signified through a variable ex- 
pression, as is a described individual; but a universal is no more 
completely determined for thought through description than is 
an individual. A description of “friendship” to a man who had 
not had a friend, or of “color” to a man who had not seen 
color, would contain a residuum of uninterpreted meaning which 
could not be eliminated by description alone. And yet univer- 
sals differ from individuals in that they can be known as spread- 
_ ing out through many perceptual wholes; they can be identified 
and re-identified as persisting elements in the process of change; 
they can be distinguished and redistinguished from other uni- 
versals. But once an individual has passed from perception, it 
cannot be again identified as the same individual. This is why 
universals can be determinately referred to through single 
words, if not through descriptions. Every universal, since it is 
self-identical, — itself and nothing else, —has its distinctive per- 
ceptual flavor; description points the way, but does not take 
the place of the presentation of these universal objects. 


Vil 


There is an apparent line of separation between descriptions 
and proper names or single symbols, and in Mr. Russell’s theory 


124 SYMBOLISM AND TRUTH 


this separation becomes extreme. Mr. Russell believes that 
proper names (or single symbols) have meaning both in and out 
of a context, while descriptions have meaning only in a context. 

“By an ‘incomplete symbol,’” says the Principia Mathe- 
matica, “we mean a symbol which is not supposed to have any 
meaning in isolation, but is only defined in certain contexts. . . . 
This distinguishes such symbols from what (in a generalized 
sense) we may call proper names. ‘Socrates,’ for example, stands 
for a certain man, and therefore has meaning by itself, without 
the need of any context. If we supply a context, as in “Socrates 
is mortal,’ these words express a fact of which Socrates himself 
is a constituent. But in other cases this simple analysis fails.” } 
These are the cases in which a phrase such as “the author of 
Waverley’’ is employed. Such expressions in themselves are 
meaningless; they have meaning only in use. 

This theory is contrary to ordinary interpretations of lan- 
guage. “The author of Waverley” is capable of standing on its 
own feet as a significant symbol; one feels no need of a context 
to give it a meaning. The phrase is used in speech as if it were 
equivalent to the proper name “Scott,’’ and like the proper 
name, it is construed as significant both in itself and in a con- 
text. Mr. Russell’s view is not supported by common sense or 
usage; it is proved by a number of ingenious arguments which 
raise fundamental questions as to the nature of meaning. An 
examination of these arguments discloses a wholly different way 
of distinguishing between descriptions and proper names (in a 
generalized sense).“The former are analyzed references or mean- 
ings; the latter, unanalyzed references. Neither depend on their 
contexts for significance. At the same time, we discover that a 
reference to an individual through a proper name is no more 
determinate than a reference to an individual through a descrip- 


tion. 
1 Whitehead and Russell, Principia Mathematica (1910), i, 69. 





DESCRIPTION AND ANALYSIS 125 


One of Mr. Russell’s most plausible arguments for the view 
that descriptions have meaning only in use is the following: 
“Take, for example, the following proposition: ‘Scott is the 
author of Waverley.’ This proposition expresses an identity; thus 
if ‘the author of Waverley’ could be taken as a proper name, and 
supposed to stand for some object c, the proposition would be 
‘Scott is c.’ But if c is anyone except Scott, the proposition is 
false; while if ¢ is Scott, the proposition is ‘Scott is Scott,’ which 
is trivial, and plainly different from ‘Scott is the author of 
Waverley.’” * The conclusion is that “‘the author of Waverley’ 
cannot mean the same as ‘Scott,’ or ‘Scott is the author of 
Waverley’ would mean the same as ‘Scott is Scott,’ which it 
plainly does not; nor can ‘the author of Waverley’ mean any- 
thing other than ‘Scott,’ or ‘Scott is the author of Waverley’ 
would be false. Hence ‘the author of Waverley’ means nothing.” 
Such expressions have a meaning in use, but not in isolation. 
In use, e.g., in the proposition, “Scott is the author of Wav- 
erley, “the phrase becomes significant when the proposition is 
understood to mean “‘x wrote Waverley’ is always equivalent 
to “x is Scott.’” | 

There is no doubt that propositions in which descriptive 
phrases occur can be translated into propositions in which these 
phrases do not occur. A descriptive phrase can always be elim- 
inated. But this is a symbolic device, and not a proof that the 
descriptive phrase in itself has no meaning. Usage holds that 
“Scott”? means the same as “‘the author of Waverley,” that both 
are significant in isolation from a context, and that “Scott is the 
author of Waverley” is not, on this account, either a trivial or 
false proposition. Common usage employs a descriptive phrase 
interchangeably with a proper name which it takes to stand for 
the same object, and common usage can be defended. 

The judgment, “Scott is the author of Waverley,” is analytic 

1 Op. cit., p. 70. 


126 SYMBOLISM AND TRUTH 


in form. It is of the form, « = (yR), which expresses an identity 
of meaning between two symbols, or two concepts. But the sym- 
bol on one side of the identity (if it refers to an object) refers to 
the object as a single and unanalyzed thing, while the symbol on 
the other side refers to it as a group of elements — as a complex 
whole which can be broken up into parts. By substituting x for 
(yR), which must be possible if these are identical in meaning, 
the identity x = x can be derived, and this is trivial: it is the 
law of identity, which is presupposed in the use of x as a symbol. 
But this does not necessitate the conclusion that either z means 
something other than (yR) or (yR) is meaningless. The conclu- 
sion to which it does lead is this: that « (if it means an object) 
means the same object as (yf), but means it in a different way; 
that the same object can be meant in two different ways, that is, 
it can be referred to analytically or unanalytically; and that the 
exhibition of an analysis — or of different analyses of the same 
object — is never trivial. If “Scott is the author of Waverley” is 
either trivial or false, on the usual interpretation of these sym- 
bols, the equation 2 + 2 = 4 is also trivial or false, for it is an 
analytic judgment of the same general form. It asserts that 
what is meant by the complex 2+ 2 is the same as what is 
meant by the symbol 4; it permits the substitution of 4 for the 
complex 2 + 2, and yields the identity 4 = 4.7 


Vit 


The judgment is accused of being trivial because it seems not 
to be synthetic; it seems to add nothing to its subject through its 
predicate. But a judgment which is analytic in form can be syn- 
thetic in effect, when one side of the identity expresses an analy- 
sis of what is represented on the other side without analysis (or 
through a different analysis). 


1 This assumes that the equations of arithmetic represent identities, which 
is, we believe, the correct view. 





DESCRIPTION AND ANALYSIS 127 


Single words or symbols can mean a great deal more than we 
are explicitly aware that they mean, and this is because we can 
refer to an object as a whole without referring to the parts or 
aspects of the object. To describe an object, which is originally 
signified by a single word, is to add to our knowledge a knowl- 
edge of the fact that the object is composed of elements. To 
signify the same object in these two different ways is expressly 
to state that the object has certain lines of structure, that a cer- 
tain analysis of it is possible. Now one can be aware of an object 
without expressly representing to himself its lines of structure, 
its possible analyses. Therefore, such a judgment of identity, 
though it takes the analytic form, x = (yR), is synthetic in 
effect. It asserts more than x = x. Statements of identity that 
present an analysis of what is meant without analysis by a single 
symbol are the only means by which indefinite concepts can be 
made definite, the only way in which meanings can be defined. 

But is a description an analysis? If analysis is breaking up an 
object into its parts, is not the discovery that an object is an in- 
stance of a universal, or that a certain description fits it, some- 
thing other than analysis? 

I can analyze an object into parts, a, b, and c, which are re- 
lated in a certain way. I can discover that my ink-well is com- 
posed of a small glass jar with a glass cover, and this seems to be 
genuine analysis. But if I find that the ink-well is black and that 
it is on the table, I am discovering relations and qualities which 
attach to it, and these do not seem to be parts in the same sense. 
And if I now describe it as “‘a black object on the table,” I do 
not appear to be analyzing the ink-well. 

This is a superficial distinction. Whether its blackness and its 
position on the table are “parts”’ of the ink-well depends on the 
point of view. These may be, on one definition, external to the 
object and, on another definition, internal to it. If by “the ink- 
well”? I intend the bare z, the individual term — what Locke 


128 SYMBOLISM AND TRUTH 


would have called its “‘substance”” — then the fact that it has a 
glass container and a small glass cover is as external to it as the 
fact that it is black and on the table. But I can mean by “the 
ink-well”’ either the individual, the z alone, to which certain 
predicates attach, or I can mean the individual taken with more 
or fewer of its predicates and relations. And this is possible be- 
cause the individual, though it may not be completely deter- 
mined by its predicates and relations, is continuous with them. 
They enter into the individual. Any predicates or relations of an 
object are “parts” of the object in a logical sense, for they par- 
tucipate in the object; and when the object is described, it is 
analyzed as a complex whole in which these qualities and rela- 
tions are elements. The bare individual, the x, of which the 
predicates and relations hold, becomes one element along with 
others. 

Description is then analysis, but it may be analysis which 
leads to an enlargement of concepts — of the meanings of single 
words or ideas, or of groups — through the discovery of new 
characters and relations that can be included in the definition. 
If I make the judgment, “Scott is the author of Waverley,” in 
ignorance of the fact that Scott wrote Waverley, what this judg- 
ment tells me is that I can enlarge my concept of Scott to in- 
clude the authorship of Waverley. I must so enlarge my concept 
if the judgment is to be true; for if I do not now mean the same 
thing by “Scott” as by “the author of Waverley,” Iam certainly 
in error. 

The meaning of a single symbol can be indefinitely expanded 
to take in more and more of the predicates and relations of an 
object, so that judgments of the form, x = (yR), continually 
widen knowledge by giving new definitions, new analyses, of 

* This explains the surprise of George IV (mentioned by Mr. Russell) when 


he learned through a mere statement of identity that Scott was the author of 
Waverley. 








DESCRIPTION AND ANALYSIS 129 


concepts which have hitherto been used with a restricted or un- 
analyzed meaning. 


IX 


The most restricted possible concept of an individual is that 
of an x—a mere “this” — devoid of all characters and relations, 
a concept which is framed only by abstraction from the con- 
crete, qualified, and related data of perception. Scott, though a 
single word is used to refer to this person, is a complex object. 
He has many aspects beyond his bare individuality, he is an in- 
dividual of this sort or that sort, and this has been shown to be 
true of all individuals. Every individual is a vortex of characters 
and relations. When one uses a proper name for an individual, 
he cannot in the beginning mean an z, shorn of all relations and 
characters, for no such thing comes into experience to be named. 
“Scott,” at the very least, originally means an («R), a complex 
of predicates individualized in a term. Thus, from the outset, a 
proper name is equivalent in meaning to a minimal description 
of the object to which it is applied. Though the bare individual 
is an element in the whole, it is the whole which is named, and 
not the individual alone. To break up this whole and take the 
meaning of the proper name to be the z to which the characters 
and relations attach, and only this, is to reduce the significance 
of the name to that of an z. “Scott,” if it means merely the indi- 
vidual, a “‘this” which is distinct from all other individuals and 
absolutely unique, is a variable; and the fact that the name is 
treated as if it had one, and only one interpretation, does not 
eliminate this indeterminateness, for it does not tell us what 
this interpretation is. 

No view of knowledge is more inadequate than an extreme 
nominalism, which holds that individuals can be picked out, 
apart from their characters and relations, and referred to 
through determinate concepts, or given distinctive names. And 


130 SYMBOLISM AND TRUTH 


yet the opposite extreme is equally inadequate, vzz., that the 
individual, or any other object, is nothing but its characters and 
relations. The attempts to reduce terms (whether individual or 
universal) to their predicates and relations, and the inverse — 
to reduce predicates and relations to their terms — are destined 
to failure because they destroy the logical frame-work of fact. 
The theory of “internal relations” cannot show that terms can 
be dispensed with in describing the world, without abolishing 
all distinctions and all description. If all relations and predi- 
cates completely absorb their terms, everything becomes one 
and indistinguishable. But it is possible to interpret the “‘inter- 
nality of relations” in another way. The wholeness of fact is 
such that the element of unity — the predicate or relation — 
enters into the terms as well as into the fact. This unity of the 
terms with the predicate or relation leaves both distinct for 
knowledge; it is not inconsistent with the externality or dis- 
tinctness of terms and relations which is necessary to logical 
structure. But at the same time, the unity of predicates with 
their terms makes it possible to include in the definition or de- 
scription of a term a reference to more or fewer of its predicates 
and relations. 

Where, it will be asked, does this extension of concepts 
through the description of objects by new characters and rela- 
tions end? It would seem that a meaning must eventually be- 
come coextensive with all the predicates of the object meant, 
that “Scott” or any other name must finally mean an object 
taken with an indefinite number of predicates. No characters or 
relations of the object would then be external to the meaning. 
This would be the necessary outcome of broadening a concept 
to its utmost possible limits. The name “Scott” would then 
signify anything which could be said about the individual, Scott; 
so that any judgment into which “Scott” entered would be- 
come analytic and trivial in Mr. Russell’s sense. 





DESCRIPTION AND ANALYSIS 131 


X 


Just as a judgment may be analytic in form and synthetic in 
effect, so a judgment may be synthetic in form and analytic in 
effect. Judgments such as “‘z has the relation R to y,” where R 
is not identity, or “x has the quality Q,” are, in general, taken 
to be synthetic, to add something to their subjects through their 
predicates. But if the meaning of'z already includes the relation 
R to y or the quality Q, the judgment is synthetic in form only. 
Its effect is analytic. Thus Kant’s example of an analytic judg- 
ment, vzz., “body is extended,” is synthetic in form but analytic 
in effect because the attribute of extension is by definition 


included in the meaning of the term “body.” If I mean by 


“Scott,” among other things, “the author of Waverley,” then 
the seemingly synthetic proposition, “Scott wrote Waverley,” is 
analytic in effect. 

Whether the predicate of a judgment adds something to what 
is meant by the subject depends, therefore, on what one means 
by the subject. This is why “Scott is the author of Waverley”’ or 
any similar statement of identity can convey more to the mind 
than “Scott is Scott,’ and why “body is extended” or “Scott 
wrote Waverley” can convey no more than “body is body” or 
“the author of Waverley wrote Waverley.” 

It is only because we do not know (analytically) what we can 
mean by a proper name or single word, or because we use them 
with a deliberately restricted meaning, that any judgments are 
synthetic in effect. Ignorance is the great restricter of mean- 
ings, and ignorance renders certain properties external to ob- 
jects, which on different definitions of these objects, become 
internal to them. One usually means by a word something 
less than an object with all its possible predicates and relations, 
and so the object can be viewed as entering into new relations 
and acquiring new predicates. “Napoleon conquered Europe” 


132 SYMBOLISM AND TRUTH 


shows Napoleon in a new réle, and is a synthetic judgment 
(both in form and in effect), if one does not include “‘conqueror 
of Europe” in the meaning of the name “Napoleon.” But this 
is an arbitrary or accidental restriction of the meaning. 

What has been said of the analysis of the meaning of proper 
names is true also of single words which stand for universals. A 
universal can be described, or it can be represented by a single 
word. The description means the same thing as the single 
word, but means this analytically, while the word means it un- 
analytically. The word is capable of being extended or con- 
tracted in meaning to take in more or fewer of the predicates 
and relations of the universal meant. A word which signifies a 
universal may enter in judgments of synthetic or analytic form, 
and these judgments will be synthetic or analytic in effect ac- 
cording to the interpretation put on the word. 

That single symbols (proper names in a generalized sense) 
can mean the same objects as descriptions, and that the state- 
ment of such identities of meaning is highly fruitful for knowl- 
edge, rather than trivial, are, then, the consequences of this 
view of description as analysis. It follows, also, that proper 
names (in the more restricted sense of this term), if they mean 
bare individuals, are of no more use to thought than 2’s and y’s 
whose values are not known. And even when their meanings are 
wider than such references to bare individuals, proper names 
give us no more determinate, or invariable, knowledge of indi- 
viduals than do descriptions. Whatever can be referred to 
through invariable symbols is universal. Aristotle himself, to 
whom individual substances were the sole realities (God only 
being excepted), believed that universals alone were the objects 
of screntzfic knowledge. What can be said of individuals must be 
said in universal terms, and only when reference to individuals 
is dropped is knowledge completely freed from variability of 
meaning. Completely determinate knowledge is of universals 





DESCRIPTION AND ANALYSIS 133 


and their connections. Hence perceptual knowledge is never 
completely determinate, never wholly compressed into the con- 
cepts of invariable meaning which function in perception; and 
yet it is the only concrete knowledge, that is, the only knowledge 
in which the individual merges with the universal. Complete 
conceptual determination and concreteness do not go together; 
what is completely determined for conception is never concrete, 
and what is concrete is never completely determined in con- 
cepts. 


XI 


Knowledge in universal terms tends to become analytic in 
form, for here, as elsewhere, concepts enlarge themselves by in- 
cluding more and more of the predicates and relations of the 
universal meant. To the layman, water is something wet, color- 
less, tasteless, and odorless; if he were asked to define it, he 
would describe it in this way. But if he studies chemistry, he 
finds that water is made up of hydrogen and oxygen in definite 
proportions, and his concept must be enlarged by the judgment 
that “water is H.0,” a judgment of analytic form but synthetic 
effect. He will discover that water boils at 212° Fahrenheit under 
atmospheric pressure, and at lower temperatures under lower 
pressures, etc.; and these facts, together with countless others, 
must be included in his concept. In the end his concept of water 
will completely sum up his knowledge of it. The word “water’”’ 
will mean all that water is known to be and do, and a judgment 
about water, ¢.g., that water boils at 212° Fahrenheit under at- 
mospheric pressure, will tell him no more than is included in his 
concept. It will be an analysis of this concept. 

Thus the chemist, if he discovers a property or law which is 
“external to” water as he conceives it, will straightway take this 
property or law into the meaning of the term. But in addition, 
there will always remain a perceptual “somewhat” to which the 


134 SYMBOLISM AND TRUTH 


name “water” belongs, and this “somewhat” will be spread out 
in numberless individual instances. But the evasive element of 
individuality will never be a part of the meaning of the universal 
term. The concept will include much that can be known only by 
inference from the perceptual properties of water; these inferred 
properties, ¢.g., molecular and atomic structure, etc., will also 
be described in universal and invariable terms. 

A science becomes analytic in form for this reason: it tends so 
to broaden its concepts of a subject-matter, originally given in 
perception, that an analysis of what is meant by these concepts 
states the laws of the science. The subject-matter is defined as 
that which follows the laws; anything which does not obey the 
laws is not included in the scope of the science. Thus matter, 
originally in perception something solid and extended, becomes 
anything that conforms to a certain set of principles — physical 
principles; and mind becomes anything that conforms to an- 
other set of principles — psychical principles. 

The drift toward the analytic form is especially evident in the 
mathematical sciences. Crude perceptions of a spread-out and 
diversified something called “space” are enlarged by the dis- 
covery of principles which can be exactly stated in universal 
terms, and which can be interpreted as referring to these percep- 
tions. “Space” is finally conceived as that system of objects 
which obey geometrical axioms and postulates; and, when 
space is thus defined, to say that space conforms to geometrical 
laws is to say merely that “space is space.” If different sets of 
axioms and postulates which can be equally well interpreted by 
the original experience are discovered, these axioms and postu- 
lates will define different kinds of space — Euclidean, and the 
numerous varieties of non-Euclidean space. Thus it becomes a 
trivial and analytic statement to say, e.g., that the parallel pos- 
tulate holds for Euclidean space, for Euclidean space is defined 
through this postulate and others. But to say that this postulate 











DESCRIPTION AND ANALYSIS 135 


holds for space as such is to raise the question as to whether the 
Euclidean analysis of space is the true analysis, and so to force 
a choice between this type of geometry and other types. The 
judgment, “Space as such is Euclidean space,” though analytic 
in form, is not a trivial statement of identity. It purports to add 
something to knowledge by showing that what we originally 
meant by “space” is truly analyzed by the Euclidean axioms 
and postulates. This judgment is synthetic in effect and can be 
proved or disproved by experience. 

A science which assumes the analytic form does not lose its 
experiential content, and this is no less true of the mathematical 
sciences than of the physical, biological, or psychological sci- 
ences. Number and space, though they may be defined through 
the laws of arithmetic and geometry, are still objects (univer- 
sals) met with in experience. A “‘science” which had no point of 
application in presented objects would not be a science, but an 
uninterpreted or partially interpreted system of symbols (or 
concepts). The description of the subject-matter given in the 
laws, the postulates and axioms, must be anchored in experi- 
ence; the variable terms, the z’s and y’s, described must mean 
something apart from the descriptions in which they appear. 
Thus if Euclidean space is simply the x which the postulates of 
Euclidean geometry describe, one does not know fully what this 
z is. There may be many different objects, e.g., certain series of 
numbers, etc., which are possible values of this x. These postu- 
lates become the laws of space only when they are interpreted 
by the spread-out and diversified something called “space.” 
The only reason why one can speak of the postulates of Eu- 
clidean or non-Euclidean geometry as postulates of geometry is 
that they are rooted in an original experience of space. 

An uninterpreted or partially interpreted system of concepts 
is merely the possibility of a science. It becomes an actual sci- 
ence only when it is taken to be a description (or an analysis) of 


136 SYMBOLISM AND TRUTH 


some field of presented objects. The fact therefore that a science 
tends to become analytic in form does not free it from the neces- 
sity of binding itself to experience by a synthetic judgment — a 
judgment which conveys the information that the subject- 
matter as perceived is the subject-matter as described. 


XII 


A second argument by which Mr. Russell supports his theory 
that descriptive phrases are without meaning excepting as they 
occur in a context, brings up the problem of “‘reference to the 
non-existent,”’ that is, of how symbols can be used significantly 
when there is no object which they mean. 

“Suppose we say: ‘The round square does not exist.’ It seems 
plain,” says Mr. Russell, “that this is a true proposition, yet we 
cannot regard it as denying the existence of a certain object 
called ‘the round square.’ For if there were such an object, it 
would exist: we cannot first assume that there is a certain ob- 
ject, and then proceed to deny that there is such an object. 
Whenever the grammatical subject of a proposition can be sup- 
posed to be meaningless without rendering the proposition 
meaningless, it is plain that the grammatical subject is not a 
proper name, that is, not a name directly representing some ob- 
ject. Thus in all such cases the proposition must be capable of 
being so analyzed that what was the grammatical subject shall 
have disappeared.” ! And this argument is carried still further: 
the Principia Mathematica asserts that a function (a predicate) 
which is universally true may nevertheless not be true of an 
object described as “‘the so-and-so.” Though it is true of every 
object that it is an identity, it is not true of “the round square” 
that it is an identity. This object is therefore nothing. 

But if the round square is nothing, does it follow that “the 
round square” is without meaning? Are not the two phenomena 

1 Whitehead and Russell, Principia Mathematica, i, 69. 





DESCRIPTION AND ANALYSIS 137 


of significance, to be without meaning and to mean something 
non-existent, different phenomena? 

There is an air of contradiction in the idea of meaning or re- 
ferring to the non-existent. But this semblance of contradiction 
disappears if “reference to the non-existent”’ is more accurately 
described as the significant use of symbols where there is no object 
for which they stand. It is possible to employ symbols signifi- 
cantly (with syntactical significance) when there is no object to 
which the group as a whole refers, and this is what Mr. Russell 
denies or overlooks. But even if it were true that a phrase which 
“means a non-entity”’ is without meaning, it would not follow 
that because some descriptions mean non-entities, all descrip- 
tions mean non-entities and are therefore without meaning. If 
“the round square”’ is a meaningless expression because there 
are no round squares, this fact does not imply that “the Presi- 
dent of the United States” is meaningless because it is a de- 
scriptive phrase of the same form as “the round square.” 

However, the important question is— Can a description, or 
a symbolic group, be significant and yet not refer to an object? 

The Principia Mathematica, being concerned with logic rather 
than epistemology, does not analyze the concept of meaning. 
But certain assumptions as to the nature of meaning seem to be 
implicit in its earlier, more strictly philosophical sections. So far 
as we can disentangle these assumptions, the view of meaning 
seems to be this: that groups of symbols which state proposi- 
tions, and proper names (in a generalized sense), are the only 
symbols which have meaning in themselves. Thus descriptive 
phrases fall between two stools: they are groups of symbols, but 
they do not state propositions; they play a part like that of 
proper names, yet they are not proper names. If this is the as- 
sumption of the argument which rejects descriptive phrases as 
meaningless outside a context, the conclusion must be granted. 
It then becomes necessary to translate descriptive phrases into 


i PON 5 EE a 


———— 


138 SYMBOLISM AND TRUTH 


another form, that is, to treat them as significant only when 
they occur in propositions, and to construe these propositions 
as statements which make use only of proper names (in the 
generalized sense). But the possibility that groups of symbols 
which do not state propositions, and yet are not proper names, 
might be significant in their own right is not considered. And 
this is what we have been urging all along: that there is some 
legitimate sense of the term meaning other than those senses 
which appear to be assumed in the Principia Mathematica. This 
type of meaning—syntactical significance—covers both prop- 
ositions and descriptive phrases; and just as a group of symbols 
which states a proposition may as a whole refer to no object, 
so a descriptive phrase may as a whole refer to no object and 
yet be significant. 

While proper names and single words, that is, simple symbols, 
unless they are defined through symbolic groups, arouse inten- 
tions directed toward objects — intentions which depend on the 
existence of these objects — a symbolic group, on the contrary, 
arouses an intention which is a function only of subordinate in- 
tentions and of the structure of the group. The meaning of a 
symbolic complex does not depend on the existence of an object 
for which it stands as a whole. In order that a symbolic group 
may be significant, it is necessary only that its constituents be 
significant (or be definable in terms of significant complexes) 
and that it have a form. It is in this sense of meaning that 
“France loves Germany” has meaning. There is no object, 
France loving Germany, but the phrase is significant because its 
constituents are significant and grouped according to a plan of 
logical structure. 

To say that a description “means a non-existent object” is a 
convenient but inaccurate way of speaking, for a “non-existent 
object’’ would not be an object and could not be referred to. 








DESCRIPTION AND ANALYSIS 139 


The clearer manner of statement is that a description can be 
significant apart from any reference, as a whole, to an object. 
“The round square” means roundness and squareness attaching 
to a term which is symbolized by a variable; it means “‘z as 
modified by roundness and squareness.” “‘The king of France”’ 
means “‘y as modified by the kingship of France.”’ And whether 
or not any such unities of terms and predicates exist to be re- 
ferred to is beside the point. Mr. Russell’s argument must be 
countered by a broader conception of meaning. 

It is because the existence or non-existence of an object sig- 
nified does not affect the significance of a symbolic group that 
“to mean a non-entity” is not to be meaningless. Only simple 
symbols which refer directly to objects require the existence of 
an object meant. Such symbols mean “‘categorically,” but syn- 
tactical or group meaning is “hypothetical,” for it presupposes 
no object corresponding to the group as a whole. 

To assert that “the round square does not exist”’ is not, then, 
to assume that there is an object called ‘“‘the round square” in 
order to deny its existence. Nor does the truth of this assertion 
lead to the conclusion that the phrase “‘the round square”’ is in 
itself meaningless. 

1 As for the statement of the Principia Mathematica, i, 87, that the law of 
identity does not apply to descriptions, 7. e., that one cannot say “the round 
square is identical with the round square,” this depends on what the as- 
sertion of identity means. It has been shown above that z = z, as a general 
principle of symbolism, means that the symbol z is always to be interpreted in 
the same way, whether or not it stands for an existent object. Thus “the 
round square = the round square” does not necessarily assert the existence of 
this object, but it does assert that the significance given to this phrase must be 
the same in all contexts; that “the round square” can be substituted for “‘the 
round square”’ in any discourse, without an alteration of the meaning. But if 
““the round square is identical with the round square” is interpreted existen- 
tially, to mean that “‘the round square has identity,” this will not be true un- 
less the round square exists. However, the symbolic interpretation of the law 
of identity is separable from the existential interpretation: “x is x”’ need not 


be construed as predicating identity of an object meant by z. See above, 
ch. II, see. vii. 


140 SYMBOLISM AND TRUTH 


XILIT 

The particles “all,” “‘every,” and “each”’ introduce a new 
idea: that of classes. 

“All men,” “every man,” “each man,” are different ways of 
referring to the class men. As in the case of the other particles, 
these particles have no meaning in themselves; they must ap- 
pear in connection with symbols that refer to universals or com- 
plex predicates. They do not signify constituents of the fact 
represented by a phrase in which they occur; they are signs of 
interpretation. Just as “the” tells us that one and only one in- 
stance of a universal is meant (though this instance is indeter- 
minate), and “a” that one among many possible instances is 
meant, so “all” tells us that the universal is signified in a certain 
manner of its occurrence — in its occurrence in a class. 

Classification rests on universals. Though a universal is some- 
thing distinct from any or all of its instances, though it is an 
aspect which can be singled out and made an object of reference, 
nevertheless, a universal occurs in instances, it modifies a num- 
ber of terms; and a class is the universal taken in conjunction 
with the terms it modifies. It is a plurality of terms modified by 
the same universal. Any predicate determines a class — the 
class of the terms to which this predicate attaches. A relation de- 
termines a number of classes: “A hates B” is, for example, a 
case of the class of ‘“‘hatreds’”’; but from this relation the class 
of ‘‘those who hate B” and the class of “those whom A hates” 
can also be derived. “‘A is between b and c”’ is a case of the class 
of “‘relations of betweenness,”’ but it also determines a class of 
“those objects which are between 6 and c” and “those objects 
between which a occurs.” In every case a class is a plurality of 
terms modified by a single quality or relation.’ 

But a class is at once a plurality and a unity. It derives its 


1 A class of one member is the only exception; this is not a plurality of mem- 
bers: but if it is a class, it is a totality of one. 





DESCRIPTION AND ANALYSIS 141 


unity from the presence of a predicate in a number of distinct 
terms, and its plurality from the distinctness of the terms. The 
difficulty of conceiving a class as an object, says the Principia 
Mathematica, is connected with the “ancient dilemma of the 
One and the Many.” “If there is any such object as a class, it 
must be in some sense one object. Yet it is only of classes that 
many can be predicated. Hence, if we admit classes as objects, 
we must suppose that the same object can be both one and 
many, which seems impossible.” 1 But the impossibility is less 
real than apparent. It is no more present in the conception of a 
class than in the conception of any object which is analyzed into 
constituents, broken up into parts which form a whole. Every 
analyzable object is both one and many, a unity of diverse ele- 
ments; and if one balks at the problem of the One and Many, he 
must reject all analysis. 

The unity of a class, however, is different from the unity of a 
fact (or a group), and for this reason a class, though it is none 
the less an object, is not the same kind of object as a fact. It is 
an object of a different order. “Caesar loving Brutus,” “‘Bos- 
ton’s being near to but north of New York,” are expressions 
that stand for factual groups. In these groups the universal 
unites the terms so that (taken with the universal) they become 
a single instance of this universal. The predicate which deter- 
mines a class unites the members in no such way as this. (But if 
there are classes there will also be factual groups, and if there 
are factual groups there will also be classes.) The unity of a 
class is of the peculiar kind called totality, and this is a new prim- 
itive idea — the defining idea of classes. 

A class is a universal in the totality of its instances, that is, it 
is an object like “man” as it appears in this sort of unity with 
diverse terms. “Man” means a universal apart from its in- 
stances, that is, in abstraction; but man is not only separable 


1 Whitehead and Russell, op. cit., i, 75. 


142 SYMBOLISM AND TRUTH 


from its instances, it is also joined to them, spread throughout 
them. “Men” as distinguished from “‘man” means the universal 
as it is particularized in a multitude of different terms. This 
object is one, and can be referred to through a single symbol, 
because the universal gives it the unity of totality, though this 
is a “looser” unity than that of a single fact of diverse terms. 
No part or selection of the terms to which a universal attaches 
is a class, a totality, through the presence of that universal 
alone. Every universal determines one and only one totality. 
Thus a portion of the class men would be a class only through 
the presence of some other predicate than man, e.g., the predi- 
cate, brave man, or strong man. A class therefore is nothing short 
of a universal in its concrete entirety. The universal, in making 
the instances one, makes them a totality, but at the same time 
permits them to be distinguished as instances. 

It follows from this notion that a class is not a sum of objects. 
The expression, “a and b and ¢, etc.,”’ does not designate a class, 
for objects which do not belong to the same class can be thus 
added together. A mere summation of objects will not give us a 
class predicate which determines them to be a totality. “The 
table and the chair and the book, etc.,” are not a class through 
the fact of being conjoined; they become a class only if there is 
some predicate which gives them the unity of totality. If they 
are “‘all the objects in this room”’ or “‘all the objects I now see,” 
they are a class. Nor does the similarity of objects alone make 
them a class, although objects of the same class are similar. 
Only if x and y and z, etc., are “all the objects similar to a given 
object c,” do they form a class, and in such cases this class will 
be a totality determined by a predicate. 

Classes are cross-sections of the world of fact. Only very lim- 
ited classes are presented in their wholeness; most classes can 
be known only conceptually or symbolically, that is, as the (x) 
totality determined by such and such a predicate. Though “all 








DESCRIPTION AND ANALYSIS 143 


men” means one object, no one has known all men; and thus 
classes seem not to be objects, but constructions of the mind. 
Yet the inability of knowledge to grasp most classes as totalities 
in perception does not disprove the objectivity of classes. The 
idea of totality once being given, —as it is in the restricted 
totalities of presentation, — this idea can be extended to totali- 
ties that lie beyond presentation, and to infinite totalities. 

“Each” and “every” as well as “all’’ precede expressions 
that refer to classes, but the distinctions between ‘“‘each,”’ 
“every,” and “all” are difficult to draw. The difference seems 
to be one of emphasis. “All men are sinful’? appears to empha- 
size the fact that the class of men is a totality. “Every man is 
sinful”? means the same, that is, that all men are sinful, but em- 
phasizes the plurality of the class. “‘Each man is sinful” also 
emphasizes the plurality of the class, but at the same time seems 
to include a reference to an enumeration of the members. But 
whatever the shades of difference in the meanings of “each,” 
“every,” and “all” may be, these three words indicate manners 
of reference to classes. 

A reference to a class is clearly a description of the form “the 
so-and-so” rather than “‘a or some so-and-so.” The totality is 
meant through an undetermined x which has only one possible 
value, that is, the totality in question. “All persons”? means 
“the (x) totality determined by the predicate ‘person’”’; this 
expression is not susceptible of many interpretations as is “a 


299] 


person. 


XIV 


The discussion of description and analysis has brought out 
the following points: 


1 It is plain that a class could have one member or an infinity of members 
and still be a totality. ‘‘ All the numbers which, when added to a number give 
that number,” designates a totality of one member — the number zero. “ All 
the objects which can be put into one-to-one correspondence with the natural 
numbers”’ designates an infinite totality. 


{ 





144 SYMBOLISM AND TRUTH 


The line of cleavage between proper names or single symbols 
and descriptive phrases is determined by structure alone; the 
distinction is not that proper names (in a generalized sense) 
have meaning in themselves, while descriptive phrases have 
meaning only in a context. Description is analysis, for the predi- 
cates and relations of a term are logical “parts” of it, and what 
is represented analytically by a descriptive phrase is represented 
unanalytically by a proper name or a single symbol. This agrees 
with common usage, which treats proper names as equivalent 
in meaning to descriptive phrases. Syntactical significance is 
present in all symbolic groups, and only when this type of mean- 
ing is neglected (or confined to groups which state propositions) 
does the contrary view, that descriptions have no meaning in 
themselves, become plausible. 

Symbolic groups are significant apart from the existence or 
non-existence of objects meant, for their meaning as a whole is 
a function of the meanings of their parts and their logical form, 
and nothing else. This wider notion of meaning covers that of 
descriptions outside a context. If there is no object correspond- 
ing to a description, this fact does not deprive the description of 
its syntactical significance. ““To mean a non-entity,” that is, 
to be significant when there is no object signified, is not to be 
meaningless. 

A description signifies a term, together with a predicate or 
complex of predicates attached to this term; but the term is 
represented by a variable which, in language, is understood to 
be present through the sign of interpretation (the particle) pre- 
ceding the phrase. Descriptions are of the general form (xR): 
the object has this structure and the symbols themselves take on 
this structure if the variable, which is understood, is supplied. 


99 «66 


Thus ‘‘a man” means “a human 2, some friend’? means 
“some friendly y,” “the president” means “the presiding 2.” 


The term described becomes the center of a complex of char- 


99 66 








DESCRIPTION AND ANALYSIS 145 


acters and relations, and the variable through which this term is 
signified is to be interpreted in the sense indicated by the parti- 
cle. “The” means that the variable has only one possible value. 
“A” and “an” mean that it has many possible values; “‘any,” 
that the value is to be chosen at random from among these many 
possible values; and “some,” that it is to be chosen according to 
an unspecified condition of selection. 

Though a description does not state a fact, it always has 
reference to a fact — to the fact through which the object in 
question is described. “‘The president of the United States”’ re- 
fers to the fact that “someone presides over the United States”’; 
“‘a bard of the sixteenth century,” to the fact that “someone 
wrote poetry in the sixteenth century”; “a man,” to the fact 
that ‘someone is human.” And whether the description signifies 
an existent object, or refers to no object, will depend on the truth 
_ or falsity of the propositions which assert these facts. ‘This is the 
basis of Mr. Russell’s reduction of descriptions to the form of 
| propositions which make assertions about terms. 

_ But it is not necessary to translate the description into an- 
_ other form to observe that it refers to a fact as well as to a term. 
The term is, as it were, viewed through the fact; the fact is 
viewed as centering about the term, so that the term assumes a 
pivotal rather than a subordinate place in the fact. (‘This is sym- 
bolized by writing the x both inside and outside the group 
through which it is described. Thus (a((xR)Sa)) indicates that 
the z is described through the whole complex ((xR)Sa).) This 
centralization of the fact about a single term is the only differ- 
ence between the fact as it appears in the description and as it 
might appear in some other (non-descriptive) form of expres- 
sion. If a description is asserted, — and it follows from this view 
that descriptions can be asserted, —it will be seen that the de- 
scription may state a fact, the fact on which the description is 
based. “The president of the United States is,” affirms the same 


146 SYMBOLISM AND TRUTH 


fact as “someone presides over the United States”; “the author 
of Waverley is,” makes the same assertion as *“Someone wrote 
Waverley,’ where “someone” is taken to have only one possible 
value. “A man is”’ affirms no more nor less than “someone is 
human.”’ ! The difference in these assertions is one of form only, 
and not of content. Therefore descriptive phrases are not dis- 
tinguished from “‘propositions”’ through the fact that the latter 
mean complexes of terms and predicates or relations, while the 
former mean only terms. Both stand for complex wholes (if they 
stand for any objects); both mean facts. 

Variable significance, which is always present in descriptions, 
is a distinct kind of meaning, different from syntactical meaning 
or from direct reference to objects through simple symbols. The 
variable, meaningless in itself, is construed as a symbol because 
it enters as a constituent in a significant whole; it is a symbol 
which arouses no specific intention, but which must be treated 
as symbolic because of its setting. And if it is given a value this 
can be, by the principle of identity, one and only one value. The 
variable is no more open to an equivocal interpretation than any 
other symbol. A variable may, however, have many possible 
values, and it will then be ambiguous — a means of attaining 
generality of reference. 

Both universals and individuals can be described, and both 
are variably (indeterminately) signified by descriptions. But an 
individual is still variably signified when it is given a proper 
name, for the proper name must be defined through a descrip- 
tion, which contains a variable element; otherwise the name 
would stand merely for a “this” of presentation and would be 
even less determinate in meaning than if it were defined through 
a description. 

The only data of perception which can be represented by 


1 “Ts” as a sign of assertion in these expressions adds or subtracts nothing 
from the meaning of the phrase. 








DESCRIPTION AND ANALYSIS 147 


invariable symbols are universals, and so the only knowledge 
which is completely free from variability of meaning is knowl- 
edge in universal terms, that is, abstract statements, laws, which 
make no reference to individuals. 

Definitions are analytic in form. They are statements of iden- 
tity, such as a = (#R); and they can be reduced to the form 
a = a. But they are not on this account trivial, since their effect 
is synthetic; they add to the knowledge of the object meant, a 
knowledge that it can be analyzed as (rR), or that predicates 
which were originally external to the meaning of a can be in- 
cluded in this meaning. Concepts of restricted meaning enlarge 
themselves through such statements of identity by taking in 
more and more of the predicates of the object meant, and in 
this way knowledge tends to become analytic in form. It tends 
to sum up all that can be said of an object in the very concept 
(the very name) of the object. But the postulates and axioms of 
a science do not completely determine the subject-matter of the 
science, even though an analysis of what is meant by “the sub- 
ject-matter” may be a statement of the laws of the science. 
Knowledge of analytic form must be anchored to experience by 
a judgment which is synthetic in effect — which asserts that the 
objects within a certain field of experience are the objects thus 
analyzed. Euclidean or non-Euclidean geometry is geometry 
because its postulates can be interpreted in terms of the experi- 
ence called “space.” 

Lastly, there is a type of object — a class — which is referred 
to by descriptions prefaced by “all,” “every,” and “each.” 
Classes are not groups, not wholes of the form (Rab ...), but 
a class is nevertheless one through the presence of a universal 
in terms. Its unity is of the undefined sort known as totality. 
Classes, with the exception of the limited totalities given in per- 
ception, are known only conceptually, that is, through symbols, 
as “‘the (x) totality determined by such-and-such a predicate.” 


148 SYMBOLISM AND TRUTH 


Descriptions, then, do not stand apart from other symbolic 
expressions. All symbolic groups have significance in themselves, 
and this significance is independent of the existence of an object 
meant. The possibility of using symbols significantly, either in 
descriptions or in propositions which are not descriptions, when 
no “real” object is referred to, lies at the basis of the distinction 
between truth and falsity. Meaning becomes truth when it is 
joined to existence; it becomes falsity when it is severed from 
existence; but without meaning there is neither truth nor 
falsity. 








CHAPTER V 


TRUTH AND FALSITY 


I 


Trourn and falsity are properties of symbols. A symbol is 
true if it stands for an object; it is false if it is significant, yet 
stands for no object; or, in the words of Thomas Hobbes, “True 
and false are attributes of speech, not of things . . . truth is the 
right-ordering of names.” ! If the term “speech” is widely 
enough construed, this definition of the aim of knowledge is a 
corollary of the theory of meaning that has been presented. The 
“right-ordering of names” is building symbols into structures 
that correspond to structures of fact, and this correspondence is 
truth. 

Belief and disbelief do not alter the truth or falsity of sym- 
bolic expressions, for the existence of meaning is a sufficient as 
well as a necessary condition of the existence of truth. No one 
can be in error unless what he believes has meaning, and he can- 
not be convicted of error if his meaning is misunderstood; nor 
can he believe truly unless that which he believes is significant. 
Yet truth and falsity are independent of belief; any idea that 
can be entertained is either true or false. Once a meaning is 
fixed, its truth or falsity is fixed; and meanings are carried only 
in symbols. This is the idea behind Hobbes’s definition. Yet it 
must not be forgotten that a symbol is more than a mark, a 
sound, a gesture, or an image; it is any of these together with 
the effect it has in a mind, that is, together with the psychical 
attitude to which it gives birth. Symbols are concepts, and to 
say that truth is a property of symbols is to say that it is a prop- 
erty of concepts. 

1 T, Hobbes, Leviathan, Part I, ch. 4. 


150 SYMBOLISM AND TRUTH 


Truth, moreover, cannot be defined without some reference to 
reality or existence; ideas, thoughts, perceptions, are true when 
they present or represent what 7s. To apprehend a truth is to 
apprehend the existence of something meant. Thus knowledge 
from the outset is directed toward reality, and finally toward 
a metaphysical goal. Epistemological questions project them- 
selves toward metaphysics through the concept of truth. But 
one must approach metaphysics humbly. He must begin with a 
limited concept of the real, which he may alter or abandon in 
the light of further criticism; for a theory of the relation of 
knowledge to reality can have no basis except in an analysis of 
knowledge as a phenomenon, and this analysis leads to a limited 
notion of reality and of truth. 

The definition here set forth is of this sort. Truth as reference 
through symbols to existent objects may be a reference to ob- 
jects that are, metaphysically speaking, only “appearances”; 
or if these objects are not appearances, they may be objects that 
are not separable from knowledge, they may be mind-objects 
only. And there are many other metaphysical contingencies 
which the definition ignores — to which it is, in Mr. White- 
head’s phrase, “closed.” 1 It adopts a restricted concept of exist- 
ence, and this yields a restricted concept of truth, whose im- 
mediate claim to acceptance is that it is workable in science, 
mathematics, and every-day thought, whether or not it is finally 
able to withstand metaphysical scrutiny. 


II 


The examination of this definition — of the notion of exist- 
ence in terms of which it is stated, together with the tests of 
truth to which it gives rise — can be better understood if it is 
prefaced by an inquiry into another view of truth: the view that 
truth is not a property of symbols, but of entities which are 


1 A. N. Whitehead, The Concept of Nature (1920), ch. 1. 








TRUTH AND FALSITY 151 


neither symbols nor existing objects, yet which have a being in 
themselves. 

On this theory, it is to “propositions” that truth attaches, 
and a proposition is not thought of as a symbol or symbolic 
group coupled with the psychical set or intention it arouses in a 
mind. A proposition is independent of psychical processes; it is a 
meaning, but a meaning considered apart from its setting in a 
mind. It is something distinct from symbols, to which they 
refer, and yet it is not an object. The proposition thus conceived 
enters as a tertiwm quid between the symbols, in which it is con- 
veyed, and the datum or object, of which it is true. It is a wedge 
which opens the way for a new class of entities — subsistent en- 
tities — which are to be distinguished from objects. The pe- 
culiar manner in which these subsistents are apprehended is 
said to be conception; to conceive is to know something, to refer 
to something, but not to refer to an object. On this view, the 
initial reference of conception is to a subsistent proposition, and 
the proposition in its turn may or may not be directed toward 
an object. If the proposition is directed toward an object, if the 
tertium quid meant by the symbols exists as well as subsists, it is 
true; otherwise it is false. 

This theory purifies truth of all psychical elements. Truth and 
falsity are not determined in any sense by the act of thought; 
they belong only to these independent entities, which can be 
thought of but are not created by thinking. At the same time, 
truth and falsity are not taken to be properties of objects, so 
that the difficulties of one type of view, which says that there 
are “false objects,” are avoided. 

The most convincing arguments for the assumption of these 
subsistent entities are derived from the consideration of false 
and negative propositions. Mr. G. E. Moore puts the case for 
them in the following way: “How can a thing ‘appear’ or be 
‘thought of’ unless it is there to appear or be thought of? To say 


152 SYMBOLISM AND TRUTH 


that it appears or is thought of, and yet that there is no such 
thing, is plainly self-contradictory. A thing cannot have a prop- 
erty unless it is there to have it. .. . When I think of a unicorn, 
what I am thinking of is certainly not nothing; if it were nothing 
then, when I think of a griffin, I should also be thinking of 
nothing, and there would be no difference between thinking of a 
priffin and thinking of a unicorn. But there certainly is a differ- 
ence; and what can the difference be except that in the one case 
what I am thinking of is a unicorn, and in the other a griffin? 
And if the unicorn is what I am thinking of, then there certainly 
must be a unicorn, in spite of the fact that unicorns are unreal. 
In other words, though in one sense of the word there certainly 
are no unicorns — the sense, namely, in which to assert that 
there are would be equivalent to asserting that unicorns are 
real — yet there must be some other sense in which there are 
such things; since, if there were not, we could not think of 
them.” } 

The status of propositions, on the view in question, is that of 
Mr. Moore’s unicorns and griffins; they are entities which are 
“‘there”’ in some sense, though plainly they are not “there”’ in 
another. They are objectives, which may be real or unreal; which 
subsist rather than exist.? 

Subsistence is a kind of being to which existence may be 
added, but to which existence is not necessary. In the realm of 
subsistence, the lion and the unicorn lie down together. To think 
of a lion or of a unicorn is to think of entities that partake 
equally of this impartial being, this thinner reality, which in- 
cludes the possible and the imaginary as well as the real. 

1G. E. Moore, “The Conception of Reality,” in Philosophical Studies 
(1922), p. 215. 

2 The terminology is that of A. Meinong’s gegenstandstheorie. Two among 
Meinong’s important works on this subject are: Untersuchungen zur Gegen- 


standstheorte und Psychologie (1904, Leipzig) (a collection of studies by several 
authors including Meinong), and Meinong’s Uber Annahmen (1902, Leipzig). 


- ee 





TRUTH AND FALSITY 153 


Ii 


The concept of the “objective” springs from what appears to 
be a logical necessity in the analysis of meaning. Meaning must 
have an objective reference, and it is thought therefore that 
there must be a thing meant wherever there is significance. If 
meaning is reference to something —a relation in which the 
mind is only one term — unless this relation is to disappear, 
it must terminate in a referent. This is the idea behind Mr. 
Moore’s statement that “to say that (a thing) .. . is thought of, 
and yet that there is no such thing is plainly self-contradictory.” 
When the referent is a non-entity, it cannot (if the argument is 
pursued) cease to be a referent; it must therefore have some 
status. It is not nothing, for if it were the meaning relation 
would collapse, being deprived of one of its terms. 

Furthermore, the reference of symbols is not merely to psychi- 
cal states, to images, to the content of the mind. The very es- 
sence of the meaning activity is that through it the mind reaches 
out toward something other than its own states;1 and yet, if 
this “something” is to be grasped, it must be somehow given. 
It must have a being which allows it to be referred to when it is, 
in some sense, not a presented or existent content of the mind. 
It must be “‘there” in some way and not “there” in another; 
otherwise meaning loses its objectivity of reference and becomes 
intra-psychical in the narrowest meaning of the term. 

But the dilemma here is not so sharp as it appears. Objectiv- 
ity of reference does not require the assumption of subsistent 
(and sometimes unreal) entities as the second term of the mean- 
ing relation. The reference of a symbol, either simple or com- 
plex, can be directed beyond the mind’s content when the entity 
referred to is in no way presented or “‘there’’; and a complex 

1 That is, toward something other than its own present states. This does 


not preclude the metaphysical hypothesis that all objects referred to are ulti- 
mately ‘“‘mental”’ in a wide sense of the term. 


154 SYMBOLISM AND TRUTH 


expression can have an objective reference when there is no ob- 
ject or objective to which the expression as a whole refers. 

Consider, first, the meaning of simple symbols which stand 
directly for objects. The theory of objectives assumes that these 
symbols, no less than complex expressions, have significance 
through reference to subsistent entities. It is not sufficient that 
the meaning relation shall have been grounded in an existent 
term; it must continue to be grounded in a subsistent one. Now, 
if to mean something is to intend it, to take an attitude of mind 
appropriate to it, the continued being in any sense — either as 
a subsistent or existent entity — of that which is meant is not 
necessary to the meaning. Indeed, anticipating or intending is 
just the sort of reference to objects that is compatible with the 
absence, as well as the presence, of what is referred to. Meaning 
is not a static relation between the mind and any sort of entity. 
It is an activity, and this activity has a direction away from the 
mind’s present content, whether or not there is a given object 
(or objective) in which it terminates. The direction of a meaning 
is determined once an object has been the terminus of the activ- 
ity; the activity continues to intend, to be appropriate to this 
object thereafter, when the object is absent or non-existent. It is 
sufficient therefore that the things which simple symbols mean 
shall have existed; the subsequent use of these symbols does not 
demand the persistence of their referents, either as subsistent 
objectives or existent objects. A meaning can be carried by an 
intention alone, and the reference does not lose its objective 
direction. 

A second type of meaning is that of complex expressions. If 
the mechanism of conception is analyzed (as it has been) into 
the grouping of symbols, the groups as a whole continue to 
refer, to mean — and to mean something other than a present 
psychical content — whether or not there exists or subsists an 
object or objective to which they refer. The meaning of a sym- 








TRUTH AND FALSITY 155 


bolic group has been shown to be a function of other mean- 
ings, together with a scheme of logical structure. A number of 
subordinate meanings enter into a unity to form a new meaning, 


‘ 


which cannot be described as a simple “‘mind-referring-to-ob- 
ject-or-objective,” as Mr. Moore would describe it; for the 
situation is made complex by a new factor — a plan of structure 
by which the symbolic elements are welded into a whole. If _ 
there is an object referred to, the reference is indirect. The sym- 
bolic group is a construction which is not taken, in its entirety, 
to stand for an object as a single word or proper name might be. 
From the direct references of the elements to things that exist 
or have existed, the mind fashions a secondary reference — a 
reference composed of references. Thus I build up the group, 
“the snow will melt to-morrow’”’; I join the several direct refer- 
ences of the words, whose meanings are determined by previous 
use, into a single indirect reference of a certain form; but I can 
know only to-morrow whether this secondary reference does or 
does not terminate, as a whole, in an object. 

If there is an object corresponding to the whole expression, 
this object will be both a unity and a plurality, a whole of parts; 
e.g., the unified fact, “the melting of the snow on the morrow.” 
But if there is no such unified object, the parts will still exist 
(or will have existed) as a plurality; e.g., there will be a to- 
morrow, and there have been snow and melting. Therefore the 
meaning of the group will be grounded in a reference to objects. 
The significance of the expression will be directed toward some- 
thing other than the present content of the mind, despite the 
fact that it corresponds in its entirety to nothing. 

It is in this sense that the false statement, “Shakespeare 
wrote The Critique of Pure Reason, has an objective reference. 
wrote,” “The Critique of Pure Reason,” stand 


99 <¢ 


“Shakespeare, 
for objects. These references to existent things, or to things that 
_ have existed, lend objectivity of reference to the whole. They 


156 SYMBOLISM AND TRUTH 


give it a foundation in fact, though it corresponds to no fact. 
And since the symbolic elements of any significant group must 
stand directly for objects which exist (or have existed), or must 
be definable in terms of symbols which stand thus for objects, 
no symbolic group is without an existing locus of reference of 
the sort that the primary, direct act of meaning demands. The 
_ meaning of the group cannot collapse into a total absence of re- 
lation to the objective world, for the objects meant by the ele- 
ments of the group are in this world and thus determine the 
mind to have a direction beyond itself. 

This is not all. The plan of structure is no less objective than 
the constituents meant by the simple symbols, even if there is 
no fact which combines these constituents in this structure. The 
logical form intended is presented, and exists, in the symbolic 
expression as a universal of which the group is itself an instance. 
The structure meant is identical with the structure of the con- 
cept, that is, of the symbols; and it is equally as real, equally as 
objective, in its conceptual or symbolic instance as it would be 
in a non-conceptual or non-symbolic instance, for it is the same 
in both. 

The fixity of complex concepts arises from their logical form. 
Given a certain form in certain symbols whose individual mean- 
ings are determined, and the meaning of the concept is deter- 
mined. If there is an object whose elements are the ones meant 
by the simple symbols, and whose structure is identical with the 
structure devised by the mind for this group, this object will be 
the thing meant. But there need be no such object; the meaning 
is still fixed and still turned toward the world of objects. The 
mind, once it invents a concept, is bound by it. The concept 
seems to become external to thought, to pass over into a realm 
beyond the mind’s caprice; for the form of the concept, though 
it is constructed in thought, is a universal which may appear 
elsewhere. The constructive activity of the mind is exercised in a 








TRUTH AND FALSITY 157 


medium which is not purely of the mind — in the medium of 
logical form. Instead, therefore, of saying that thought arbi- 
trarily assigns meanings to complex concepts, as it does to single 
words or signs, one can say that these concepts assign meanings 
to thought. The logical structure of the concept reaches out 
toward objects and, as it were, selects the one (if there is one) to 
which the concept corresponds. The structure of the concept 
means the structure of the fact because it is identical with the 
latter. And so the verification of a complex expression is a search 
in the direction of the objects meant by the constituents of the 
expression for an instance of the same logical form which is 
present in the expression. Thus the mind invents its concept 
but discovers their truth or falsity. 


IV 


The tertitum quid which, on the theory of subsistence, is as- 
sumed to intervene between symbols and their objects disap- 
pears in this analysis of meaning. It is absorbed in the symbols 
themselves. Meaning is not, as the theory of objectives would 
have it, what is referred to through symbols; it is the referring 
itself, that is, the meaning rather than the meant. And this act 
is always turned in the direction of existing objects, even though 
_ there may be no single object in which it finds its fulfillment; so 
that meaning does not become purely a relation of one psychical 
event to another. It is an act in which psychical events point 
beyond themselves, and symbols are the perceptible embodi- 
ments of this act. 

Not only are symbols the instruments of knowledge, they are 
of its very stuff. Mediate knowledge and a large part of immedi- 
ate knowledge are words, images, signs, taken with the effects of 
these in minds. There is no independent thing called “knowl- 
edge,’ which words, images, psychical attitudes, signs signify. 
_ The act of knowing itself, in so far as it is not pure awareness, is 


158 SYMBOLISM AND TRUTH 


the use of symbols. To assume that there is some such thing as 
the “proposition” or “objective,” which is the referent of sym- 
bols but which is itself neither a symbol nor an object, is to 
postulate a detached element of “meaning” as the terminus of 
thought. All attempts to catch this elusive and independent 
“meaning” end in the capture of images, of words, of attitudes 
or sets of the mind. The view that propositions are what sym- 
bols signify, that they are meanings apart from symbols and 
from the mind in which these symbols have significance, cuts 
off meaning and hypostatizes it, as if it might have being in 
itself; but this is as impossible as that a picture might exist 
without the canvas on which it is painted. 

The elimination of these subsistent entities subserves the end 
of economy of assumption. Truth is to be found in the two-term 
relation between symbols and objects; the proposition as a third 
entity is not needed. Symbols either signify existent objects or 
no objects, for the phrase “existent object” is a tautology, and 
the phrase “non-existent object” is a contradiction. The cate- 
gory of objectivity is not wider than the category of existence; 
there are no non-existent entities of any sort. And yet it is possi- 
ble to speak or think significantly without assuming an object 
thought or spoken of. 

It is this notion, that a concept need not have an object, 
which supports Kant’s refutation of the ontological proof of 
God and makes ontological arguments in general invalid. No 
concept implies the existence of an object conceived. But the 
theory of subsistence restores the ontological argument in a rare- 
fied form. Though one cannot, on this theory, argue from a con- 
cept to the existence of an object, he can always argue to the 
subsistence of an objective. “A thing must be in some sense to be 
thought of.” This gives every concept a referent with a being — 
a being which is often non-existence. A strange multiplication 
of ontological types! One sort of being should suffice. If a thing 








TRUTH AND FALSITY 159 


does not exist it has no being; to speak of it as subsisting is 
merely to attempt to smuggle it back into reality, from which it 
has been once dismissed. 

An expression which “means a non-entity”’ stands, then, for 
no sort of entity; but it is still an expression which has signifi- 
cance and an objective reference, apart from the existence or 
subsistence of any corresponding referent. 


V. 


Under what conditions is reality or existence predicated of 
objects? What are the criteria of objectivity? 

The first criterion of existence, as the term is used in the 
present definition of truth, is perception. In perception, some- 
thing is given to the mind, there is a datum; and it is to this 
datum that existence belongs. And yet an uncriticized percep- 
tion does not guarantee the reality of its object. Dreams, illu- 
sions, hallucinations, are no less vivid and convincing than 
waking or normal presentations; they are no less perceptions in 
which something is given. But one cannot say that a dream 
object or an illusory object is really what it appears to be. 

Perception is complex; the datum is only one element in it. 
- What seems to be given as a datum may be largely the creation 
of concepts, of signs with their attendant mental attitudes, at 
work in the perception. For an object perceived is always an 
) object meant, referred to, intended by, a concept. Concept and 
datum blend to form a presented whole, and what is merely in- 
tended or meant cannot easily be separated from what is given. 
Perceptions must be criticized, and only some of them can be 
accepted as presenting objects which are really what they seem 
to be. 

I am walking in a forest, let us say, and I see at some distance 
the body of a man across my path, which proves on closer in- 
spection to be the trunk of a fallen tree. What I first saw had the 


160 SYMBOLISM AND TRUTH 


appearance of being given; yet it could not have been wholly 
given or it would have resisted further examination. The percep- 
tion was an elaboration of data. Images, and perhaps unspoken 
words, together with their meanings, fused with the data; the 
mind automatically organized these elements into a whole, so 
that the data were presented under a concept — they were per- 
ceived through a meaning. Not only was this the case with the 
perception of the recumbent body; there is every reason to sup- 
pose that the perception of the tree-trunk was also an elabora- 
tion of data. Here, too, concepts were added to what was given, 
the data were viewed through a meaning, the presentation being 
no less complex; and if I believe the fallen tree-trunk to be a 
real object, it cannot be on grounds of its givenness alone. 
Perception is a union of sensation and conception. Sense data 
are the simplest observable elements in perception; with them 
the analysis of a presented whole comes to an end, though it is 
difficult (and often impossible) to disengage these sense data 
from their settings. The sense data are obviously supplemented 
by something non-sensory. They are signs which, in the lan- 
guage of Thomas Reid, “suggest” what is perceived. Take an 
extreme example: I hear a footstep outside my closed door and 
perceive that someone is about to enter the room. The sensory 
elements are plainly much less than the whole perception. The 
sound may not be a footstep, it merely “‘suggests” a footstep; 
and certainly it may not be the footstep of someone who is about 
to enter the room. This is clearly a conceptual addition to the 
sense data. Now what is true in the extreme case is true also in 
other cases. One perceives, for example, that it is raining; but 
the sensory constituents of this perception are not the whole 
fact, that it ts raining. There are sensations of dampness, of 
grayness, of cold, of faint vertical motions in the field of vision; 
and these sensations together with what they mean make up 
the fact. They awake in the mind, as do the words on a printed 


TRUTH AND FALSITY 161 


page, certain intentions carried by images and half-uttered 
words; they cause one to take an attitude which is appropriate 
not only to dampness, to cold, to grayness, but to a whole of 
which these are parts; and thus they mean that it is raining. 
The effect of them is as if they caused one to formulate this 
proposition.! 

The sense data and the concepts, moreover, come into a pe- 
culiar unity in perception. They coalesce, and the elements that 
are sensed infect the conceptual elements, so that a large part of 
what is conceived seems also to be sensed. An excellent illustra- 
tion of this is the perception of space; we seem actually to see 
depth, though there is no doubt that much, if not all, of the per- 
ception of depth is a conceptual elaboration of sensory elements. 
The sense data are both signs to which concepts attach and 
parts of the objects which these concepts signify; and in the 
perception of a complex object or fact the sensory elements fall 
into their proper places as constituents of a whole which is both 
conceived and sensed.” 

The presented whole, nevertheless, has the appearance of 
simplicity. The fact that it 1s raining seems to be given in its en- 


1 Reid adds that in perception we believe “‘irresistibly”’ in the reality of 
what is presented, and so perception becomes judgment, being conception 
joined to belief. But perception need not include belief. One often doubts the 
evidence of the senses; yet the doubt does not do away with the perception. 
Further, an illusory perception persists when it is disbelieved; this is indeed 
the very reason why it is illusory. It is nearer to the fact to say that we tend to 
believe our perceptions, that the perception tends to become a judgment, 
rather than that it is a judgment. Belief is a new attitude of mind, and one can 
withold belief in his perceptions. If perception produces immediate and “‘irre- 
sistible”’ belief, this is a belief that usually gives way to doubt — a belief that 
does not persist unless it is substantiated by other evidence than the givenness 
of the perception in question. See T. Reid, Essays on the Intellectual Powers of 
Man, Essay II, especially ch. 10. 

2 A thing, a complex object, is therefore much more than a class of sense 
data, as Mr. Russell describes it. It is a unity of sense data according to a 
definite plan of structure. The data enter into a conceptual scheme, they be- 
come parts of a meaning, and are at once signs and constituents of the object 
meant. For Mr. Russell’s view, see Our Knowledge of the External World 
(1914), ch. 4. 


162 SYMBOLISM AND TRUTH 


tirety; the tree-trunk appears to be presented as a solid, three- 
dimensional object; and even though the perception is known to 
be a fusion of data with concepts, an inspection of the presented 
object by itself does not readily separate what is conceptual 
from what is not conceptual. It may well be that the object ex- 
ists as it is perceived; that the very whole intended is given, as 
well as the sensory elements. The concepts may aid the mind to 
grasp what is actually a complex datum, rather than cut it off 
from a clear knowledge of the real object. And yet if the whole 
content of every perception is taken to be a datum, it is impos- 
sible to deny existence to the objects given in illusions, hallu- 
cinations, and dreams. If I dream that I am in Thibet and awake 
to find myself in my bed, I have been in Thibet and have been 
miraculously transported to my bed. The conclusion must be 
that, in some perceptions at least, only a part of the content is a 
datum; in illusory perceptions, the interpretation of the data, 
rather than the data themselves, creates the illusion. 

There is a compulsion in perception which is not found in con- 
ception, and this is why we conclude that a part, if not all, of the 
content of the perception is given to the mind and exists. No 
analysis of knowledge can ignore this compulsion of perceptions; 
this is their claim to be presentations of reality. Concepts can be 
altered at will so long as their references to perceptual objects 
are disregarded; they are inventions rather than data. But per- 
ceptions — even illusory and dream perceptions — are not 
purely invented. There may, to be sure, be some metaphysical 
sense in which the data of perception are created by mind; 
nothing may be completely independent of mind in the most in- 
clusive meaning of the term. The data of perception may be 
nothing more than lively and compelling psychical states — 
nothing more than Hume’s impressions; or they may be, as 
Berkeley would have us believe, thoughts in the Divine Mind. 


TRUTH AND FALSITY 163 


But this dependence on mind in a wider sense would not render 
them, if they are truly data, any the less independent of thought 
in a narrower sense, that is, of the mind’s conceptual or sym- 
bolic activity as it has been described. If conceptual activity 
created objects, there would be a real object for every thought; 
ontological proofs could not be invalid; one could not think 
without thinking of the existent, and even a phenomenal dis- 
tinction between reality and illusion would disappear. Existing 
objects in the limited sense now in question are independent of 
concepts. Yet these objects are cognized in perceptions from 
which concepts are never absent. 

The most that can be said of the reality of a datum, apart 
from the concepts through which it is known, is that it exists as 
*‘something-or-other”’; and this is self-evident and trivial, for it 
asserts merely that it is a datum. Such an indefinite predication 
of existence is not yet the cognition of an object, and is not suffi- 
cient for organized knowledge. To apprehend the reality of an 
object is to apprehend more than the existence of “something- 
or-other,”’ more than reality in general, though this wholly un- 
specified reality is the only reality that givenness alone can con- 
firm. The “something”’ which is real must be perceived to be of 
a definite nature or in definite relations to other things; it must 
be placed in reality, as well as perceived simply to exist. It will 
then be brought under a concept; it will be apprehended through 
a meaning. 

No presentation can be dismissed as totally unreal, however 
illusory its content may be. In a dream, the dream places, peo- 
ple, events, are given to the mind and they exist. But they do 
not exist as physical realities; they are dream objects only. The 
fact that I perceive palaces, gardens, and praying fakirs in my 
dream of Thibet is no illusion; the illusion is that I perceive 
these as physical rather than dream realities. The deception 


164 SYMBOLISM AND TRUTH 


vanishes when the data are differently conceptualized — when 
the whole is placed in reality as a dream.’ 

When reality is predicated of what is given in perception, this 
is always a predication of something other than bare reality; it 
is a predication of reality of a definitely intended sort. If, on the 
contrary, the content of a perception is judged to be unreal, this 
judgment does not mean that it is unreal without qualification. 
It is unreal only under some concept, ¢.g., as a “physical” or 
“external” object, etc. Bare existence belongs to every datum, 
and the question for knowledge is: How can this existence be so 
conceptualized that it fits in with other existences? 

If perception were the apprehension of data and nothing 
more, everything would be what it is perceived to be, and given- 
ness in perception would be an absolute guarantee of the reality 
of the object given as it is given. But a presentation from which 
all conceptual elements were subtracted could be only an im- 
mediate awareness of a reality that could be named or char- 
acterized in no way. The datum would not be articulately expe- 
rienced; it would be intuited rather than perceived. Truth, as a 
property of symbols that mean existent objects, is not a refer- 
ence to reality as it might be known in pure immediacy, but a 
reference to perceived objects; and givenness in perception goes 
only part way toward assuring reality to such objects. 


VI 


Do not sensations guarantee the existence of their objects, if 
perceptions do not? Are not sense data “hard,” indubitable, and 
free from conceptual elaboration? 


1 “Tife and dreams are leaves of the same book. The systematic reading of 
this book is real life, but when the reading hours (that is, the day) are over, we 
often continue idly to turn over the leaves, and read a page here and there 
without method or connection; often one we have read before, sometimes one 
that is new to us, but always in the same book. Such an isolated page is indeed 
out of connection with the systematic study of the book, but it does not seem 
so very different when we remember that the whole continuous perusal begins 


TRUTH AND FALSITY 165 


Sensationalism and empiricism have been frequently con- 
fused. It has been taken for granted that what is given in ex- 
perience is given through the senses alone and that there are no 
data but sense data. And yet, search as we may for a pure sen- 
sation, one is never found. “A pure sensation is an abstraction.””? 
Sensations appear only in the context of perception, as the sim- 
plest elements of presented wholes. Experience itself is of “a 
teeming multiplicity of objects and events,” which cannot be 
reduced to or derived from elements so thin as sense data; and 
the attempt to do so is well characterized by James as “aban- 
doning the empirical method of investigation.” ? 

To recognize a sense datum is to observe that the complex 
objects of perception can be analyzed into simpler constituents, 
but this observation does not carry the implication that these 
complex objects are (or are known as) sense data and nothing 
else.* The table on which I write is brown, hard, and rectangular; 
it is cold and smooth to the touch; yet these sensations, by 
themselves, do not give the table I perceive. The perceived ob- 
ject is more than sensory elements; it is these “thought” or 
meant together into a whole. A pure sensation, or collection of 
pure sensations, if there could be any such thing, would be as 
near the negation of experience as anything imaginable. 

Short of a purely intuitive knowledge, which would be an 
awareness of no specific object or quality — not even of some- 
thing as definite as a sensory quality — there are no cognitions 
which do not make use of concepts. The elements in experience 
which psychologists call “sensations” only approximate toward 
pure sensations. The concepts through which the content of a 


and ends just as abruptly, and may therefore be regarded as merely a larger 
single page.” Schopenhauer, The World as Will and Idea, Bk. I, sec. 5. 

1 W. James, The Principles of Psychology, ii, 1. 

2 Op. cit., vol. i, ch. 9, p. 224. 

3 The view which makes sense data the primary units of cognition speaks 
of objects, situations, facts, as “constructs” from sense data, but we are urg- 
ing that sense data are “‘destructs”’ from complex objects, situations, or facts. 


166 SYMBOLISM AND TRUTH 


sensation is apprehended may have been thinned down to a 
minimum; yet it cannot be maintained that concepts are wholly 
absent so long as sense data are known as specific qualities, so 
long even as they are definitely attributed to the senses. The 
very predicate “sensation” conceptualizes them. The cognition 
of objects, qualities, events, no matter how simple, is never any- 
thing less than recognition; the mind intends, takes an attitude 
appropriate to, the things it senses, and thus recognizes them as 
things meant. A bare sensation, ¢.g., of red, does not spring into 
my mind without a concept to meet it. My mind is prepared for 
knowing red, and the sense datum stands forth from the back- 
ground of purely immediate knowledge because “red” is what 
I mean as well as what I sense. And if I mean “red,” a sign of 
some sort is present. There is an image or an incipient vocal ut- 
terance, etc., which carries what is in effect the proposition, 
“this is red.” Through the concept, the sense datum becomes a 
part of my articulated knowledge. Sensation then “differs from 
perception only in the extreme simplicity of its object or con- 
tent’’; ! and the outer limit of knowledge is not sensation but the 
pure awareness, or intuition, which surrounds the whole act of 
concrete knowing.” 

Since conception is present everywhere in knowledge within 
this outer limit, the richer experience of objects, events, situa- 
tions, facts, has no less a claim to be taken as a datum, which 
exists as experienced, than have sensations. The true empiri- 
cism is not sensationalism. The true empiricism accepts the con- 
tent of presentations in their wholeness and makes what it can 
of them, rather than analyzing out the sensory aspects and de- 
nying reality to all that remains. Sensationalism does violence to 
experience and is the shortest road to scepticism, for, if only the 
impermanent and insubstantial data of the senses exist, reality 
speedily dissolves into a flight of subjective shadows. 


1 W. James, loc. cit. 2 See below, ch. VIII, sec. xii. 


TRUTH AND FALSITY 167 


The fact that experience in the full meaning of the term ap- 
pears only when concepts, that is, thoughts and their references, 
enter in cognition, does not make it necessary to hold that these 
conceptual factors cut us off from reality. Concepts may facili- 
tate as well as hinder the apprehension of data, for it is only by 
means of concepts that the passing sensation is arrested and 
experienced as an aspect of an object. When a landscape is be- 
fore me, I know through the concepts that I am experiencing 
trees, mountains, and a river, rather than a mere flow of sensa- 
tions. The concepts may cause me to come into a closer cogni- 
tive relation to the real, instead of causing me to misinterpret 
and misconceive the real. Thought is not a veil separating the 
mind from what exists. 

Kant shattered Locke’s conception of the mind as a tabula 
rasa; he made it evident that mind is active not passive in per- 
ception. Even Locke faltered in his “‘blank-sheet”’ sensational- 
ism. The mind, which, like a dark room with a single window 
high in the wall, has at the beginning of Locke’s Essay only one 
aperture of light, sensation, is discovered in the end to gain most 
of its “complex ideas” from comparing, relating, and abstract- 
ing the “ideas” which enter through the senses. The mind is 
found to be active. Knowledge will not submit to the tabula rasa 
description. 

At every point in experience, thought — organization in a 
conceptual scheme — is at work. Concepts, symbols and their 
intentions, bridge the gaps between this experience and that, 
between disorganized sensory presentations and integrated per- 
ceptions; and empirical reality — reality in the sense in which 
we are now speaking of it —comes into knowledge through 
what might be called “presentational thinking.” 

The view that thought isolates the mind from reality and 
leaves a thing-in-itself shivering in the empty noumenal spaces 
‘beyond experience, might possibly be true for an ultimate real- 


168 SYMBOLISM AND TRUTH 


ity. But Kant himself insists that the objects of experience, if 
they are “transcendentally ideal,” are “empirically real.” They 
are given in presentational thought, and this is their empirical 
reality. Whether or not reality is, in the last resort, inaccessible 
to thought, there must be some sense of the term “reality” 
which makes the real accessible to thought; otherwise there 
would be no objects of perception. Objects are capable of exist- 
ing, in this meaning of the term, as they are perceived through 
concepts — as presented wholes of definite characters or in 
definite relations; and truth is reference to these objects. 

Thought, therefore, may cause knowledge to approach the 
real, or it may remove it from the real. Truth in perception is 
possible for the same reason that illusion (or falsity) is possible; 
because thought is a constituent of perception. And for this rea- 
son, likewise, no perception in itself attests the existence of its 
object as it is perceived. 


Vil 


The second criterion of existence, which is a necessary supple- 
ment to givenness in perception, is consistency — consistency 
with the whole of our organized knowledge. By means of this 
criterion, the data of any single perception are fitted in with 
other data and given a place in reality, as well as judged barely 
to exist. At the same time, this criterion permits us to infer 
with more or less certainty, depending on the strictness of the 
inference, the existence of objects not given in perception.’ 
(That this criterion of existence — consistency with the whole 
of knowledge — does not render our definition of truth circular 
will be presently shown.) 


1 This metaphysical hypothesis, however, is extremely unstable, since the 
thing-in-itself can be positively characterized in no way. It is an x, of which 
one can say nothing more than that it does not appear in any experience; it is 
something other than any possible object of experience. See below, ch. VIII, 
sec. iii. 

t The whole problem of the validity of induction is involved here. But if 
any inductions are true, the objects they refer to exist. 


TRUTH AND FALSITY 169 


The axiom that there can be no inconsistency in the real is 
open to several interpretations, each of which turns on a differ- 
ent notion of reality. 

Consistency and inconsistency are relations between propo- 
sitions or concepts — that is, between symbols. By definition, 
p and q are inconsistent if, when one of them is true, the other 
is never true. No two true propositions are inconsistent. Now, 
on the assumption that an existent object is not a proposition or 
a concept, it follows that the real cannot be truly said to be eithor 
consistent or inconsistent, though the concepts through which it 
is viewed give it the appearance of consistency or inconsistency, 

The thorough-going rationalist, if he grants that reality is not 
conceptual or propositional, will still believe that a complete 
knowledge of the real through propositions would be a consistent 
knowledge. He will postulate that reality is consistent in the 
sense that it can be consistently conceptualized, even though it 
is other than concepts. The anti-rationalist, on the contrary, 
will assert that no consistent or inconsistent body of proposi- 
tions is adequate to reality; that the real is wholly beyond con- 
ceptual knowledge and is known no less truly through incon- 
sistent propositions than through consistent ones — for, to the 
anti-rationalist, neither could represent reality. Thus the thesis 
of any one of the Kantian antinomies tells us as much, or as 
little, about the Kantian reality as the antithesis; and M. Berg- 
son joyfully embraces contradictions as a means of leading the 
mind to intuitions, not because reality is contradictory but be- 
cause it is beyond the grasp of concepts and propositions. “In 
attempting to describe what we know in the abstract logical 
terms which are the only means of intercommunication that 
human beings possess, Bergson is driven into perpetual self- 
contradiction, indeed, paradoxical though it may sound, unless 
he contradicted himself his description could not be true.” ! 

1 K. Stephen, The Misuse of Mind (1922), p. 12. 


170 SYMBOLISM AND TRUTH 


Each of these interpretations of the axiom of the consistency 
of the real — the rationalistic and the anti-rationalistic — refers 
to an unlimited, an ultimate, reality. But the reality we have 
been considering is limited, and the very principle of its limita- 
tion is that it must be capable of being consistently presented 
and represented. If there are realities which cannot be consist- 
ently conceptualized, these are real in some more extended 
sense. One cannot deny Kantianism or Bergsonianism unless it 
be on metaphysical grounds; nor can he affirm the complete con- 
sistency, the rationality, of the real. It may be that empirical- 
rational knowledge floats on the surface of a world whose depths 
are reached neither in perception nor in thought. Yet it is possi- 
ble to go some distance with a less extended notion of the real, 
which makes reality rational but does not preclude a final “ir- 
rationalism.” 

We mean then by a real object one which can be given in (or 
inferred from) an experience which is consistent with the whole 
of knowledge. Such real objects can be known through concepts, 
as these concepts enter in perception; and if an object given in 
perception is really what it appears to be, its characters and re- 
lations will not have been created by the act of conception. A 
real object is independent of concepts, though it may not be in- 
dependent of mind on a much wider interpretation of this term. 
Moreover, these real objects must have a structure; otherwise, 
they could not be known through concepts, nor could they be 
consistently assimilated to the whole of knowledge. 

These are all necessary conditions of the reality of an object, 
in the present limited sense, but it must be observed that they 
are not sufficient conditions. The whole of knowledge might 
conceivably be false, and then none of the objects presented in 
such a consistent experience would be really what they are per- 
ceived to be. The most we could truly say of them would be that 
they had a bare existence, that they were not non-entities. And 





TRUTH AND FALSITY 171 


so we have not completely defined even this limited reality; we 
have merely laid down certain conditions which it must fulfil, 
we have confined it within certain boundaries. It remains still a 
basic and undefined term, necessary to the analysis of truth. 


VIII 


For Kant the limits of experience were marked by the cate- 
gories, which were necessary principles of thought, implicit in 
the act of judgment itself. But Kant’s categories are empty of 
content. The consistency of empirical-rational knowledge is 
more than a purely formal consistency, more than fidelity to the 
laws of logic — even of “transcendental logic.” Everything that 
can be thought or experienced will, it is true, obey these formal 
laws, but obedience to the laws of logic alone is no criterion of 
existence. The touchstones of the reality of what is presented to 
us are general truths which cannot be derived from the princi- 
ples of logic. They are categories, but not categories which are 
implicit in the nature of thought; no a priori deduction of them 
is possible; they are always subject to revision. 

First among these “empirical categories” can be placed the 
generalizations of common sense that is, prescientific generali- 
zations: nothing is ever both crooked and straight, round and 
square, black and white; nothing is ever before something else 
and at the same time after this same thing; nothing is ever out- 
side something and at the same time within it; everything has a 
cause; water does not flow up-hill — and countless other princi- 
ples which do not follow from the postulates of logic but which 
operate in determining the reality of objects. When I awake 
from a dream of the other ends of the earth, though the experi- 
ence has been sufficiently vivid to convince me of its physical 
reality, I conclude that I was dreaming; for I could not have 
been in two such distant places as the remote regions of the 
earth and my own bed at so nearly the same time. The dream is 


172 SYMBOLISM AND TRUTH 


inconsistent with common-sense physical categories. So long as 
I conceive these events as physically real I am unable to place 
them in experience without contradiction. 

All well-established scientific principles operate in the same 
way as the generalizations of common sense in determining the 
reality of given objects. It is assumed that if an object is really 
spatial or numerical in its nature it will not violate the principles 
of geometry or arithmetic; that no material reality would trans- 
gress the laws of mechanics, and no chemical reality the laws of 
chemistry. Every new generalization, every new theory, adds a 
further category under which reality is predicated of presented 
objects; so that experience both tests and is tested by scientific 
and prescientific generalizations. Laws, theories, and the facts 
on which laws and theories are built mutually correct one an- 
other. A generalization is verified by the existence of an object 
which conforms to it in a special instance, or by the empirical 
reality of something which can be deduced from it. At the same 
time, presented objects are accepted as real because they are 
perceived as special instances or consequences of general princi- 
ples. The criterion of the truth of theories is empirical reality, 
and the criterion of empirical reality, the truth of theories. 

We may be mistaken in our perceptions themselves, or in the 
assumptions, the body of theory, by which we estimate the real- 
ity of what is given in perception, or in both. It is always possi- 
ble that a new set of categories may completely overturn all 
previous estimations of reality. Yet the fact that all perceptions 
and all judgments are subject to error does not make it neces- 
sary to believe that no perceptions, no judgments, give us real- 
ity. When a presentation is consistent with the whole body of 
knowledge, the presumption is overwhelmingly in favor of the 
presented object being really what it is perceived to be. We can 


1 “Theory” is here taken to mean any principle or body of principles that 
exceeds the given. 


TRUTH AND FALSITY 173 


attain no more certainty than this. There is no self-evident, un- 
deniable badge of reality — unless it be of bare existence. The 
categories that operate in fixing the places of presented objects 
in reality are not a priorz and unalterable principles of reason, 
blank forms of perception and judgment. They are accepted 
universal truths which are themselves subject to error. The 
mediaeval philosopher who, when he was asked to view the spots 
on the sun through a telescope, replied — “‘I have read Aristotle 
many times and I assure you that there is nothing of the kind 
mentioned by him; be certain therefore that the spots which 
you have seen are in your eyes and not in the sun” — was cor- 
rect in method though not in fact. His categories were anti- 
quated, but within these categories his reality was consistent. 

A nice balance of theory and fact is for science the very prin- 
ciple of its life. And if the “delicate, contentious, and fantasti- 
cal”’ learning of the Middle Ages bore no fruit but the delight 
in speculation for its own sake, the worship of fact alone cannot 
bring forth even this fruit. Knowledge is a growing whole of 
fact and theory. 


IX 


If truth is the correspondence of concepts or symbolic expres- 
sions with existent objects, and an existent object is one given in 
a perception that is consistent with the whole of knowledge, is 
not the definition of truth completely circular? 

It would be circular if consistency with the whole of knowl- 
edge were identical with existence, that is, if concepts created 
their own objects. But this is not the case. The existent is in- 
dependent of the concepts through which it is known. Truth as a 
property of symbolic expressions, and existence as a property of 
objects, are not the same. Though existence can be definitely 
predicated of objects only if certain general truths are consist- 
ently applied in experience, the objects to which these truths 


174 SYMBOLISM AND TRUTH 


refer stubbornly resist being reduced to thought-creations. 
They are data given to thought but not invented by it, and 
truth is reference to reality, not reality itself. 

Consistency with the whole of knowledge is therefore a test of 
existence and of truth, but it constitutes neither truth nor ex- 
istence. Clearly, if truth is the correspondence of concepts with 
existing objects, no true generalization could be inconsistent 
with a perception of existing objects. True generalizations 
would necessarily become tests of existence. But the existence of 
objects would not thereby become a function of the truth of 
these generalizations; nor would the truth of these generaliza- 
tions be merely their consistency with perceptions of existing 
objects. The tests of truth follow from the definition; they are 
not equivalent to the definition. 

Moreover, the consistency which is a function of the truth of 
propositions ! could not define truth, for 2és definition presup- 
poses the idea of truth. And if consistency means, as it other- 
wise would, “conceivability” apart from truth or falsity, this is 
equally far from being truth. One can invent an infinity of con- 
sistent systems of concepts, if consistency is a matter of con- 
ceivability, of definition, alone. Such systems remain non-con- 
tradictory so long as the ideas in them are used with the original 
definitions, and so long as the general principles of the construc- 
tion of concepts are observed. But there is no compulsion, no 
reason other than caprice, for defining an idea in one way rather 
than another. The consistency of such a system gives it no refer- 
ence to reality; it places it merely as one among an infinity of 
“possibilities for thought.” If I find perceptual objects that can 
be consistently conceptualized in the propositions of such a sys- 
tem, the system has passed one test of truth; and if I further 
discover that it is consistent with the whole of accepted knowl- 


1 p and q are consistent if there is a case in which both are true, and incon- 
sistent if, when the one is true, the other is never true. 





— nl ——- —~- -~+ 


TRUTH AND FALSITY 175 


edge, it has passed another. Its truth is as nearly established as 
possible. But the proof of truth and truth itself are different 
things. The truth of the system is its correspondence to reality. 


D4 

The pursuit of “conceivability”” as a definition of truth leads 
to the “coherence” theory, in which conceivability finally tran- 
scends the limits of all ordinary thought. The essence of the cor- 
respondence theory is that it holds thought and reality apart, 
and the essence of the coherence theory, that it identifies them 
— that truth, reality, and conceivability become one. Coher- 
ence, as the term is used in this theory, is more than the con- 
sistency of a single science or of all sciences. It is an ideal of 
knowledge beside which all else is fragmentary and “mutilated,” 
and to which no finite knowledge attains. 

This is made plain by Mr. H. H. Joachim, who carefully dis- 
tinguishes coherence from consistency: “The ‘systematic co- 
herence,’ therefore, in which we are looking for the nature of 
truth, must not be confused with the ‘consistency’ of formal 
logic. A piece of thinking might be free from self-contradiction, 
might be ‘consistent’ and ‘valid’ as the formal logician under- 
stands those terms, and yet it might fail to exhibit that syste- 
matic coherence which is truth.” ! For Mr. Joachim, to be “con- 
ceivable” and “coherent” means to be “a significant whole”; 
and ultimately there is only one significant whole — the Ideal 
Experience, which is Reality. Nothing short of knowledge of 
this Whole, this Absolute, is Truth. There are no separable 
truths. A single isolated proposition is partly true and partly 
false; it is incomplete, and no more than a faltering step toward 
the perfection of knowledge — the one Truth. Mr. Russell, in 
criticising Mr. Joachim, pointedly asks : Is the theory itself, 
being not the whole of knowledge, wholly true? 2 


1 H. H. Joachim, The Nature of Truth (1906), p. 76. 
? B. Russell, Philosophical Essays (1910), p. 150. 


176 SYMBOLISM AND TRUTH 


Mr. Joachim’s examination of truth proves one thing cer- 
tainly: that truth, as it appears in empirical knowledge, in sci- 
ence and every-day thought, and in the despised reasoning of 
the formal logician, is not the truth he is speaking of; that a 
metaphysical criticism of knowledge passes beyond — and it 
may be reverses — a descriptive epistemology. 

The objections that Mr. Joachim levels against correspond- 
ence are instructive; they illuminate the nature of this relation.’ 
He points out that any correspondence must be a correspond- 
ence of the structure of wholes as well as of their elements. Each 
element must play the same part, fulfil the same functions, as 
the corresponding element in the other whole; and thus the two 
must be identical in structure. But he concludes that it is im- 
possible to make out any such correspondence between per- 
ceived wholes and conceptual or propositional wholes, giving as 
his reason for this that: “‘On the one side, we have a whole of 
experience at the level of feeling; and, on the other side, a whole 
of experience at the level of reflective thought. To say that there 
is (or may be) identity of structure is to maintain that these ex- 
periences are different matters subsumed under an identical 
form ... the idea of an identical structure in different materials 
is quite inadequate when applied to the wholes in question, wz., 
felt- and thought-wholes.” ? 

The conclusion which Mr. Joachim rejects is exactly the one 
that the analysis of logical form has led us to accept. Concepts, 
symbolic expressions, and presented objects are indeed “differ- 
ent matters subsumed under an identical form.” A perceived 


1 There is no doubt, as Mr. Joachim shows, that unless reality — or a kind 
of reality — were present in knowledge, the notion of truth as correspondence 
to existent objects would be an unworkable hypothesis. Locke, for instance, 
seems to be beating thin air when he describes truth as the reference of ideas 
to unknowable objects beyond ideas. Yet even this theory cannot be shown to 
be false. The most serious accusation that can be brought against it is that it is 
quixotic; that it is impossible to apply the definition as a test of truth. 

2 Op. cit., pp. 26, 29. 








TRUTH AND FALSITY 177 


whole is not merely “felt”’; perception is not on the level of pure 
awareness in which nothing articulate is given. Objects are per- 
ceived as having a certain structure, their elements are given as 
grouped in a definite order, they are composed of major and 
minor groups of distinct and recognizable forms. Reality, in the 
present sense, is rationally presented in that it is analyzable, in 
that its form is presented with it. And what Mr. Joachim calls 
the structure of “reflective thought” is embodied in the group- 
ing of the symbols in which the thought is expressed. The iden- 
tity of form in propositions (symbolic groups) and perceived 
objects brings about the correspondence of “reflective thought”’ 
with fact, which is truth. 

Correspondence it is true implies a distinctness, a separate- 
ness or externality of the corresponding wholes. Yet in percep- 
tion there is no separation of the concept, which is a constituent 
of the presentation, from the datum. Datum and concept cannot 
be disengaged and compared. Must one say that here the rela- 
tion is no longer correspondence, that datum and concept be- 
come one in “presentational thought,” where the margin of dis- 
tinctness between them is so narrowed that the object is given 
along with (or through) the proposition which is true of it? This 
is undoubtedly Mr. Joachim’s view; a perception, he believes, is 
already at the level of “reflective thought”; there is nothing ex- 
ternal to the perception to which it can correspond. 

A pure concept, that is, a proposition whose object is not 
given in perception along with it (or through it), is, on the other 
hand, clearly distinct from its object and can be said to corre- 
spond to the object; e.g., ““Napoleon escaped from Elba”’ is 
purely conceptual, its object does not accompany it, and hence 
there is no difficulty in describing its truth as correspondence to 
fact. Scientific theories, generalizations, historical statements, 
memories, predictions — the larger part of knowledge — are 
purely conceptual; such propositions are distinct from the ob- 


178 SYMBOLISM AND TRUTH 


jects of which they are true and can be said to correspond to 
these objects. But, as Mr. Joachim points out, this is an unim- 
portant type of correspondence, and it cannot be truly said to be 
correspondence — but is rather coherence — unless the truths 
of perception can be likewise shown to be genuine cases of corre- 
spondence. 

There is no doubt that in perception the proposition and the 
object cannot be torn apart, the concept fits the object as the 
die fits its cast, the two coincide as superimposed figures in ge- 
ometry might; and the only evidence of a discrepancy is the in- 
consistency of the perception with other experiences. Yet the 
relation however close must still be correspondence when the 
concept is true, for so long as the concept and the object are not 
identical they are distinct. One would be justified in giving up 
the notion of correspondence only on the hypothesis that the 
proposition and the datum are the same. And this is the funda- 
mental reason beneath the objections of the coherence theory to 
correspondence as a definition of truth: the coherence theory 
wishes to eliminate the distinction between thought, or concep- 
tion, and reality. Certainly if an existent object is identical with 
a coherently thought object, it is absurd to speak of truth as the 
correspondence of concepts with existent objects. But existence 
must be independent of concepts, where conception is anything 
short of the coherent — and unattainable — thought which is, 
for Mr. Joachim, Reality; especially, where conception is the 
significant use of symbols. For if existence were identical with 
conception, every thought would refer to a real object. We could 
not escape thinking of the existent; there would be no falsity. 
Since the existent and the conceptual are distinct, their relation 
is correspondence, however narrow the margin of separation for 
knowledge between them; nor does identity of structure make 
the proposition and its object one. 

The notion that the structure of thought is found in the sym- 








TRUTH AND FALSITY 179 


bols it uses to express itself and that this same structure perme- 
ates the world of real objects, at least the real objects which can 
be presented in a consistent experience; the further notion that 
these real objects are not identical with concepts and yet can be 
apprehended only by the use of concepts, though they may in 
this way — even in perception — be apprehended falsely; these 
ideas give a complete and simple meaning to the definition of 
truth as the correspondence of concepts to reality. At the same 
time, the notion of syntactical significance, of meaning which is 
directed toward the world of objects yet need not terminate in a 
single object or fact, permits propositions to be false without 
robbing them of their significance. Truth becomes in a literal 
sense a property of symbols, for propositions and concepts are 
symbols or symbolic groups as they function in minds. All this is 
implicit in Hobbes’s statement that “‘true and false are attri- 
butes of speech, not of things . . . truth is the right-ordering of 
names.” 
XI 

Since meaning alone is all that is necessary to truth and fal- 
sity, belief and disbelief, assertion and denial —in short judg- 
ment — fall outside the discussion of truth and falsity proper. 
Yet from one point of view, judgment is closely connected with 
truth, for no truth is genuinely known until it is judged or be- 
lieved. To know truth is to judge, but to be in doubt, to enter- 
tain ideas without assertion, to perceive without believing, is 
not to know truth. 

Assertion and denial, belief and disbelief, are secondary atti- 
tudes toward propositions. They supervene on the primary atti- 
tude of understanding, which is that of holding the proposition, 
the symbol or group of symbols, before the mind with a con- 
sciousness of their reference but without regard to whether or 
not there is an object to which they refer. To understand is to 
frame a hypothesis, to put one’s self in a state of inward prepa- 


180 SYMBOLISM AND TRUTH 


ration for an object when the mind is still in doubt as to the ex- 
istence of such an object; and here the attitude of understanding 
ends, or else passes by a gradual transition into that of belief. 

To believe an idea was, for Hume, to have it vividly present in 
consciousness; but the vividness of ideas is a cause of belief 
rather than belief itself. It is certainly true that a lively percep- 
tion of an object or an especially clear understanding of a propo- 
sition tends to become a belief. Entertain an idea for a suffi- 
ciently long time and you will believe it; 1 for belief is of the 
same mental genus as understanding. Both are preparations for 
objects, both are intentions of the mind with a direction beyond 
the mind’s present content. Belief differs only in being a more 
complete preparation, a more earnest intention. Belief is readi- 
ness to act as if the proposition which is understood meant an 
existent object. It is willingness to use the proposition as if it 
were true. 

As against Hume’s notion that belief is the vividness, insist- 
ence, or compulsion of ideas, it is only necessary to observe that 
one may suffer from a vivid illusion without believing that the 
illusory content is what it appears to be. Though one tends to 
believe anything he understands (or its negative, which is sug- 
gested by it), and particularly to believe what is given in percep- 
tion, still there is a point of transition between entertaining an 
idea or being presented with a content, and believing in the 
truth of this idea or the existence of this content. This transition 
cannot be described as a passage to clear understanding or vivid 
presentation, for the understanding may be already clear, the 
presentation already vivid. It is a transition to a new state of 
mind, to a state of mind which has something in common with 
the apprehension of meanings or of presented contents, but is 
nevertheless distinct. 

The existence or non-existence of the things our thoughts 


1 Or believe its negative, which is suggested by it. 





TRUTH AND FALSITY 181 


mean, the truth or falsity of concepts, adapts these concepts to 
uses which would not otherwise be possible. A true proposition 
can be employed as a premise in an inference in a way in which 
a proposition merely entertained cannot be employed. The 
truth and falsity of ideas makes possible a calculable and suc- 
cessful commerce with the world of fact; so that the value of 
truth is, in the first place, practical. Yet if truth is good as a 
means toward other ends, it is also good in itself — as an end 
toward which a certain intellectual interest is directed. 

But there is an intellectual interest which is wider than the 
interest in truth: this is the interest in possibilities, in fancies or 
fictions for their own sake. The apprehension of significance, 
that is, of possibilities for thought (constructive imagination) is 
the primary function of the intellect, and if the truth of these 
possibilities added to them no qualities of use or attraction, 
thought would end in hypothesis. There would be no judgment; 
the existence or non-existence of objects meant would be of no 
moment. To the dreamer, the truth of his dream is irrelevant; to 
the believer, the truth of his belief is indispensable, for the mo- 
tive of belief is the interest in truth. Thus beyond judgment lies 
pure speculation; add the interest in truth, which is the widest 
— the most impractical — of practical interests, and you add 
belief. 


XII 


Belief is more than the thought of existence coupled to a con- 
cept, and this is another reason why it must be regarded as a 
new attitude of mind, distinct from (though continuous with) 
conceiving and perceiving, however vivid and clear. To assert 
and believe that “Shakespeare wrote Hamlet” is not to entertain 
the thought of “the existence of Shakespeare’s authorship of 
Hamlet,” for this is itself a concept and not a belief. Belief and 
assertion take a step that carries the mind beyond conception; 


182 SYMBOLISM AND TRUTH 


they leap the gap between conception and existence by trans- 
forming the hypothetical into the categorical. 

This is strikingly put by Hume in a passage in which he also 
shows that a single concept (that is, on our view, a single word 
or symbol) can be true or false and can be affirmed or denied. He 
comments on the accepted definitions of conception, judgment, 
and reasoning as follows: “‘ Conception is defined to be the simple 
survey of one or more ideas: judgment to be the separating or | 
uniting of different ideas: reason to be the separating or uniting 
of different ideas by the interposition of others, which show the 
relation they bear to each other. But these distinctions are faulty 
in very considerable articles. For, first, it is far from being true, 
that, in every judgment which we form, we unite two different 
ideas; since in that proposition, God is, or indeed any other 
which regards existence, the idea of existence is no distinct idea, 
which we unite with that of the object, and which is capable of 
forming a compound idea by the union. Secondly, as we can thus 
form a proposition which contains only one idea, so we can exert 
our reason without employing more than two ideas... . Whether 
we consider a single object or several; whether we dwell on these 
objects, or run from them to others; and in whatever form or 
order we survey them, the act of the mind exceeds not a simple 
conception; and the only remarkable difference which occurs on 
this occasion is when we join belief to conception, and are per- 
suaded of the truth of what we conceive.” ! 

As for Hume’s first point, judgment is undoubtedly more 
than a union of the idea of existence with a concept. The onto- 
logical proof of God fails to produce belief because it is apparent 
that the addition of the idea of existence to that of God does not 
make the latter any the less a concept. But Hume, who is con- 
firmed by Kant on this point, is not wholly correct in saying that 
‘*the idea of existence is no distinct idea, which we unite with 


1D. Hume, A Treatise of Human Nature, vol. i, part iii, sec. 7, note. 





TRUTH AND FALSITY 183 


that of an object.” It is possible to conceive of the existence, or 
for that matter of the non-existence, of something meant; e.g., 
“the non-existence of the round-square”’ is an intelligible ex- 
pression. Existence can be a predicate, even if it is the most gen- 
eral possible predicate. The important fact is that, although ez- 
astence is a predicate which can be added to concepts, belief goes 
further than the addition of predicates to concepts. It com- 
pletely removes the concept from the area of the hypothetical. 

The second point made by Hume in this passage is of special 
interest in connection with the present definition of truth. Hume 
declares that a single idea or concept can be judged and can be 
true or false, though truth is usually thought to belong only to 
propositions and it is not customary to give the name “propo- 
sition”’ to anything less than what is expressed in a complete 
sentence. “God,” “evil,” “the king of England,” and similar 
fragmentary expressions are not commonly said to exhibit truth 
or falsity. But the difference between a word or a phrase and a 
full sentence is not that the one is capable of being true or false, 
while the other is not; the difference is that the one (usually) 
embodies an assertion or a denial, while the other embodies 
something merely understood, assumed, held before the mind 
without assertion or denial. “‘God is,’”’ “‘evil is,” are assertions 
of what is meant by “God” and by “evil.”’ The single words 
(unasserted) are therefore as much entitled to be taken as propo- 
sitions (unasserted) as are any completed sentences.! 

1 Whether we are to name single words and incomplete phrases “propo- 
sitions,”’ is a verbal question. The term “proposition,” if one so wishes, can be 
reserved for complex expressions which have the completeness of full sen- 
tences. But this will not alter the fact that the less complex expressions are 
either true or false. Propositions — even if they are held always to be complex, 
a union of subject, predicate, and copula — are unities which are affirmed and 
denied as wholes, and which are true and false as wholes. The subject-predi- 
cate logic, which asserts that the predicate is affirmed or denied of the subject, 
that it is true or false of the subject, breaks un the unity of the proposition and 


is at a loss to restore it. Yet this unity must be restored if there is to be truth. 
A proposition composed of a subject, predicate, and copula is true only if both 


184 SYMBOLISM AND TRUTH 


For some symbols, then, — for those which refer directly to 
objects and are not merely defined through symbolic groups, — 
truth and significance are the same thing. Knowledge, being 
built on elementary simple symbols which refer thus to objects, 
takes its rise from true concepts or “true symbols,” and falsity, 
which appears later, rests on truth. Only when a kind of signifi- 
cance which is other than a direct reference to objects is devised 
does falsity become possible. But any symbol, either simple or 
complex, is either true or false, and a full sentence differs from a 
fragmentary phrase or a single word only in that the former is 
asserted or judged, while the latter is (usually) simply considered 
or understood. 


XIII 


Just as the primary attitude of understanding is carried by 
symbols, so also is the secondary attitude of belief. Beliefs do 
not hang in mid-air cut off from expression. One believes when 
he expresses this attitude by some sign to himself or to others, 
and since belief is readiness to act, a natural and common sign 
of belief is action. I know that I believe most of my perceptions 
because I act as if what appears in them were really what it 
seems to be; moreover, I am often unaware of what I believe un- 
til I assert it, which shows that belief is inseparably bound to its 
expressions. 


the subject and predicate mean something existent, and — what is more im- 
portant still — only if there is an existent whole in which the predicate is 
united by the relation of predication to the subject. The fact that the propo- 
sition can be broken up into a subject, predicate, and copula is not therefore 
the reason for its being true or false. This necessary unity of meaning in a 
proposition suggests that the term “‘proposition” can be used for any whole 
which has a unified meaning, and this would not exclude single words or in- 
complete phrases. We might speak of a single word as an “‘unanalyzed propo- 
sition” in contrast to all symbolic groups, which would be “‘analyzed propo- 
sitions.”” Among analyzed propositions we should need to distinguish descrip- 
tive phrases as a special class. On this more extended interpretation of the 
term, a proposition would be any unified meaning; and since on our view 
meanings are carried only by symbols, it would be any symbol or group of 
symbols taken in its function as an instrument of significance. 





TRUTH AND FALSITY 185 


Assertion is so closely related to belief that it is impossible 
sharply to distinguish them. If there is any difference it is this: 
that assertion is the inward or outward expression of belief by a 
sign, while belief itself is the attitude expressed. A full sentence 
always contains a sign of belief: ““money is the root of all evil” 
stands for two things, for the fact and the belief in the propo- 
sition; while “money’s being the root of all evil” signifies the 
same fact without the belief. (The passage from consideration to 
belief is often marked in thought by the insertion of the verb 
“is,” or its equivalent, in the train of inward speech which 
passes and repasses in the mind.) If one openly asserts some- 
thing he does not believe, the presence of the sign of assertion is 
nevertheless calculated to produce belief in others. 

The copula or any symbolic element equivalent to the copula 
has a triple réle in judgment. Its primary function is to call at- 
tention to the truth of the proposition in which it appears, to 
signify that this proposition is believed or ought to be believed. 
Secondly, it indicates the unity of the whole, though it is not 
necessary that the copula be present in order that the propo- 
sition be taken as a whole; the syntactical signs give the sym- 
bolic group its unity of meaning. Thirdly, the copula adds the 
predicate existence to the concept. But of these three functions, 
the first — as a sign of assertion — is the essential one.! 


XIV 


Belief and disbelief appear, on first thought, to be direct 
opposites which are related to one another as desire is to aver- 
sion, approach to withdrawal, or acceptance to rejection. Yet 
disbelief cannot be the witholding of belief, for this is under- 
standing or consideration without belief or disbelief, without 
affirmation or denial. Nor can it be the dismissal of the propo- 


1 There is still a fourth meaning of the copula: its use to signify identity, 
e.g., “Scott zs the author of Waverley.” 


186 SYMBOLISM AND TRUTH 


sition disbelieved as meaningless, for an idea must be enter- 
tained if it is disbelieved. Disbelief if more than the suspension 
of judgment, the refusal to commit oneself. It is as affirmative 
as belief. 

“The true opposites of belief, psychologically considered, 
are,” in the opinion of William James, “‘doubt and inquiry, not 
disbelief”; 1 and this suggests that disbelief is really a species of 
belief. Disbelief is a belief in the falsity of a proposition, that is, 
that there is no existing object corresponding to it; and thus dis- 
belief is a belief in the truth of the proposition “‘p is false.”’ By 
the principle of the excluded middle, either p or not-p is true, so 
that “‘p is false” is equivalent to “not-p is true,” and “‘p is true” 
is equivalent to “not-p is false.’’ Hence to disbelieve a propo- 
sition, to believe that “‘p is false,”’ is in effect to believe its nega- 
tive. (And the converse is also true; to believe a proposition is in 
effect to disbelieve its negative.) Disbelief, instead of being the 
negation of a belief, is the belief of a negation. 

But if belief is an attitude of preparation, completer prepara- 
tion than understanding, for an object intended by a proposi- 
tion, how can one believe a negative? Are there negative ob- 
jects? Can one act as if something negative were in existence? 
For this is what belief in a negative would require. If I assert 
that “I have not been in China” and expect this proposition to 
be believed, the assertion must refer to some objective content 
to which the belief can be fastened. Negatives must have a point 
of attachment to existing objects. This being the case, denials 
will take a place beside assertions as positive judgments which 
are equally useful in inference and equally necessary in bringing 
about successful adjustments to the world of fact. Full-blown 
disbelief differs from belief only in the nature of the content 
toward which it is directed; it is not a different attitude of mind. 

Every proposition tends to suggest its negative. To under- 


1 W. James, Psychology, vol. ii, ch. 21, p. 284. 








TRUTH AND FALSITY 187 


stand the meaning of a proposition is also to understand the 
meaning of its negative, and hence the intention which carries 
the significance may as readily pass over into disbelief as belief. 
To entertain the idea of p is also to entertain the idea of not-p: 
it is to be in readiness for two mutually exclusive contingencies. 
The added psychical pressure of belief may be in the direction of 
one or the other, but in either case this new attitude of mind 
will be continuous with, not opposed to, the attitude in which 
the idea is merely understood or considered as a possibility. 
When it is said that any idea which is understood tends natu- 
rally to be believed, this means that either its positive or nega- 
tive tends to be believed; in other words, that the tendency to 
belief is always present in understanding but forks toward the 
two alternatives, one of which is disbelief. 

There is, on the other hand, a frame of mind in which one ex- 
periences an intellectual aversion toward accepting either the 
truth or falsity of ideas, in which he says “no” without affirm- 
ing or denying the proposition thus met; an attitude of simple 
incredulity, appropriate to strange phenomena or extraordinary 
concepts. It is this attitude which is directly opposed to belief. 
I may, like Aladdin before the hidden jewels, rub my eyes in the 
very presence of an unfamiliar sight, and be unwilling to act 
either as if it were real or unreal. This attitude, which is familiar 
to all men, completely replaces belief (and disbelief) in the mind 
of the sceptic, who knows no truth and is not even sure that he 
knows no truth. 

Incredulity supervenes on and is provoked by the survey of 
possibilities for thought, but like its opposite, belief, it is a de- 
parture from the attitude of merely considering possibilities. 
The sceptic does more than understand or entertain the ideas of 
which he is sceptical; he sets his mind against them, he inhibits 
the natural tendency to affirm or deny the propositions he holds 
before his understanding. Incredulity is a definite shrinking 


188 SYMBOLISM AND TRUTH 


from belief or disbelief, and not simply the survey of possibili- 
ties for thought; and this is why it is the genuine opposite of 
belief. Thus in a mood of pure speculation or fancy, scepticism 
has no more place than belief or disbelief. It is quite as inappro- 
priate to be incredulous of a myth or a romantic tale as to in- 
quire whether it is true or false; to be sceptical as to whether the 
Ancient Mariner shot the albatross is no less irrelevant than to 
believe or disbelieve it. Yet to the thoroughly incredulous per- 
son, the true sceptic, a world of fancy — whether it be of roman- 
tic, scientific, or metaphysical fancy —is still open. Thought can 
range where it will among possibilities, for if possibilities for 
thought were not left to the sceptic, there would be nothing to 
be incredulous of. 

Scepticism is a sophisticated philosophy because only by dint 
of much thinking, much turning over of possibilities, do ideas so 
completely nullify one another that none seems worthy of ac- 
ceptance. The unsophisticated man on the contrary is credu- 
lous, for concepts, ideas merely entertained, project themselves 
toward action and belief. Incredulity, when it is not erected into 
a philosophy, is unstable; it can play no positive part in knowl- 
edge. It can prevent us from falling into error and nothing more» 
but it can be of no use in shaping a course of action, in arriving 
at conclusions either in theory or practice, as positive denial 
can be. The “no” of the sceptic is the “no” of indecision. To 
be incredulous is to attain no end, but positively to deny a 
proposition is to believe something which may be of use. 


XV 


Belief and disbelief, denial and assertion, are the only avenues 
of approach to truth. Though truth is not manufactured by 
1 Aristotle denies even the consideration of possibilities to the sceptic, for 


he believes that one must accept the truth of the principle of contradiction if 
he thinks in any sense of the term. See Aristotle, Metaphysics, bk. iii, ch. 4. 





TRUTH AND FALSITY 189 


judgments, it does not stand out for knowledge in isolation from 
the judgments through which it is known. The cognition of 
truth, like that of beauty or good, is colored by an interest, 
which is the motive of judgment — the interest in truth. And 
just as it is possible to lose sight of the objects toward which the 
moral and aesthetic interests are directed, and to confuse beauty 
and good with the feelings they arouse, so it is possible to mis- 
take truth for the feeling of certainty that accompanies satis- 
factory belief. Truth is then reduced to a psychological state; it 
becomes a matter of intellectual taste, as beauty and good, on 
the parallel theory, are matters of aesthetic and moral taste. 

The contradiction in this psychological relativism appears in 
the answer to the question which Plato put to the Sophists: If 
belief is the measure of truth, and I believe that this is not so, do 
I not believe truly? ! There is no reply but an affirmative one on 
the Sophists’ own hypothesis, and only if the relativist is willing 
to give up the law of contradiction, does his view sustain itself. 

Scepticism, like relativism, often arises from the fact that 
truth can be known only through belief; but this philosophy, 
extending as it does no further than incredulity — incredulity 
reiterated and reinforced by incredulity — is born of too great 
rather than too little love of truth. The sceptic disdains to find 
truth in the feeling of certainty. He withholds judgment to the 
very last and does not deny truth, for he is aware that a single 
judgment — even the judgment that there is no truth, or that 
he doubts that there is truth — is like a stone cast in still water: 
the circles widen outward, embracing a more and more extended 
region, so that if one affirmation or denial is ventured on there is 
no stopping short of a theory of truth and reality. He therefore 
finds all things, perceived and unperceived, to be unacceptable 
to the intellect, indifferent to knowledge. 

Hume’s scepticism goes only part way. He is incredulous of all 


1 Plato, Theaetetus, Jowett’s translation, marginal p. 161. 


190 SYMBOLISM AND TRUTH 


metaphysical theories, but not of the psychological processes by 
which ideas are joined together and brought into relation to the 
“‘impressions’’ of the senses. Yet he is acutely conscious that 
knowledge is belief — and, it may be, nothing but belief. If we 
could attain truth, he argues, we could not be certain that we 
had, for we should still be believing. The mind, like a moth at- 
tracted by a light, trusts its impressions because it cannot help 
doing so; but that these impressions are true of a reality given in 
them or beyond them remains forever no more worthy of belief 
than disbelief. Hume sees knowledge only from the psychologi- 
cal angle, and leaves it hopelessly tossed between this “‘irresist- 
ible” idea or impression and that, but with no anchor for any be- 
lief. And Hume, too, touches the profounder scepticism that 
doubts even itself; there are revulsions from philosophy, sudden 
returns to common sense, when the most ordinary beliefs seem 
to him no better or worse than the finest-spun philosophy. 

Scepticism of this sort can be escaped but not refuted. One 
can easily imagine Hume undermining the whole structure of 
Kant’s “refutation” by merely pointing to the fact that it is 
built on belief. Scepticism, in its subtler forms, is an over-cau- 
tious, not a self-contradictory, philosophy. It refuses to take 
the leap of belief — to undergo the risk of error that is never 
absent from knowledge. 

The one final criterion of truth is our capacity to believe prop- 
ositions; though a belief may be arrived at by circuitous routes, 
the ultimate evidence of truth is the compulsion of a belief. If 
one asks for what reasons he holds a conviction, it is either on 
the strength of some other conviction, or on the inherent 
strength of the conviction itself. Try as he may, he cannot 
break the circle of his beliefs. To test truth we must assume 
truth; we must believe that there is some valid principle by 
which truth can be tested, and that there is a truth to test. 

It is not difficult for the sceptic to show the risk of defining or 








Ht 


TRUTH AND FALSITY 191 


attempting to test truth. Consider the test that has been pro- 
posed, consistency with the whole of knowledge. How complete 
must this knowledge be? Clearly, no experience is ever complete; 
there are always additions and corrections; in the light of fur- 
ther experience what now appears to be consistent may prove to 
be inconsistent. Yet if the test of truth is consistency with’an in- 
complete experience, this is too narrow; no allowance is made for 
the reversals to which any growing body of knowledge is sub- 
ject. But what could be meant by a “‘complete experience’’? Is 
this something more than a personal knowledge—is it all know]- 
edge, past, future, possible, including that of other minds, as it 
might be brought together in a single mind? If so, much as one 
might like to appeal to this complete experience, he cannot do 
so; for he can see through no other eyes than his own, and know 
through no other mind than his own; and he can know only in 
the present. The test he actually can apply is that of consistency 
in his experience at the present moment — the present including 
memories of the past; and this is only a small measure, a feeble 
approximation, to complete consistency. Furthermore, it may 
be that reality is not self-consistent, that consistency is read into 
it by the mind, that reality slips between the eager fingers of the 
intellect, leaving only a shell of empty appearances. 

But the very imperfections of this test show how the circles of 
belief strive to push outward beyond the phenomenal to that 
which can in no sense be called an “‘appearance.”’ The concept of 
truth links itself inevitably to that of reality. A truth grounded 
in anything less than a complete, a metaphysically conceived, 
reality will still be open to question in the mind that conceives 
this truth. A theory of knowledge without a metaphysics is at 
best only a partial repudiation of scepticism. If one embarks on 
an examination of truth, the security of his position will ulti- 
mately depend, not only on a faithful description of knowledge 
as a phenomenon, but on the scope of the concept of reality to 


192 SYMBOLISM AND TRUTH 


which he finally comes. He will need to complete the picture by 
a metaphysics of knowledge. 


XVI 


What has been said of truth, existence, and judgment can be 
summarized as follows: 

The correspondence of propositions or concepts with existing 
objects is truth, but a proposition (or concept) is not a subsist- 
ing tertium quid interposed between symbols and objects; it is 
the symbols themselves, taken with the intention or psychical 
set they arouse in a mind. This does not deprive the proposition 
(or symbolic expression) of an objective reference, a direction 
toward the world of objects, even though there exists or subsists 
no referent for it as a whole. For its meaning is a function of 
simpler meanings united in a scheme of logical structure; and 
these simpler meanings, being direct references to objects that 
exist or have existed (or being definable in terms of such direct 
references), give the complex meaning a direction beyond the 
mind’s present content. Moreover, the structure of the expres- 
sion codperates in determining the whole to have an objective 
reference, since the object meant (if there is an object meant by 
the whole) must be identical in this respect with the expression; 
and if the whole stands for no object, the structure, being a uni- 
versal which could occur in a factual as well as a symbolic in- 
stance, will still refer beyond itself. The assumption of subsist- 
ent entities as the termini of meanings is therefore unnecessary ; 
especially since meaning is not a static relation between the 
mind and some second term, but an activity — an activity of 
preparation or anticipation, which presupposes the presence in 
no sense of the object anticipated or prepared for. It is necessary 
only that some objects — those which are directly referred to by 
the constituents of the symbolic group — shall have been pre- 
sented, in order that complex expressions should have a mean- 








TRUTH AND FALSITY 193 


ing; these expressions in their entirety do not need to refer to 
any entity, subsistent or existent. Thus a false proposition is 
one which is significant, yet stands as a whole for no existing 
object or subsisting objective. The category of objectivity is no 
wider than that of existence. 

The term “existence” or “reality” is used in a limited sense, 
though it is not defined; and the criterion of existence, which is 
also the criterion of truth, is the presentation of an object in an 
experience consistent with the whole of knowledge. Inferences 
based on such perceptions (if these inferences are valid) permit 
us to reach objects not given in perception. Every perception 
has a datum, but the datum is always perceived under a con- 
cept. Concept and datum coalesce to form a whole of presenta- 
tion, so that what is given and exists independent of the percep- 
tion cannot be disentangled from what might be added through 
concepts, by the mind’s invention. Sense data are the simplest 
elements of presented wholes, but even these data are not purely 
immediate; the mind in recognizing them brings them under 
concepts. Therefore sensationalism, which grants existence only 
to the data of the senses and fails to observe that a sense datum 
is never known in complete isolation from presented wholes, is 
not the true empiricism; the complex perceptions of objects, 
situations, and facts have an equal claim to be taken as presen- 
tations of reality. Indeed, the concepts in perception may bring 
us into a closer cognitive relation to the real, rather than sepa- 
rate us from the real, for the mind is more than a blank sheet on 
which objects write impressions. 

No presentation in itself guarantees to its datum anything 
other than bare existence, reality of an indefinite sort; but it 
does guarantee this thin reality even to the data of dreams, illu- 
sions, and hallucinations. When the data are apprehended as 
objects of this or that sort, or in this or that relation (as they 
must be apprehended if they are to enter into organized knowl- 


194 SYMBOLISM AND TRUTH 


edge), a further criterion of existence than givenness is needed. 
The data must be placed in reality under a concept which makes 
the presentation consistent with the whole of knowledge. 

This consistency with the whole of knowledge is a criterion of 
existence for this reason, that the existence which gives truth, in 
the present meaning of the term, to symbolic expressions is re- 
stricted to objects which can be consistently conceptualized, 
which can be fitted into rational knowledge without contradic- 
tion. This does not assumé that reality is finally self-consistent, 
or that it can be completely known through consistent concepts. 
Nor does it assume the contrary, that neither consistent nor in- 
consistent concepts are adequate to the real. That the existent 
is capable of being consistently presented and represented is the 
limiting condition of the notion of reality on which this defini- 
tion of truth rests, but it need not be a condition of a more ex- 
tended reality. 

Consistency is determined not by the laws of logic alone, or 
by formal “categories,” but by general truths, empirical cate- 
gories, which are subject to revision and reversal. All well-estab- 
lished scientific principles and a host of prescientific generaliza- 
tions operate as tests of the reality of perceived objects. The 
criterion of the existence of objects is the truth of theories, and 
the criterion of the truth of theories is the existence of objects. 
Theory and perception mutually support and correct one an- 
other. This fact does not make the definition of truth circular. 
Truth is correspondence to reality, and so it follows that per- 
ceptions of existing objects will be consistent with general 
truths, but it does not follow that existence is a function of 
these truths, nor that truth and consistency are the same. Con- 
sistency is a test of truth but is not equivalent to truth. 

The “coherence theory” rejects correspondence as a defini- 
tion of truth because this relation implies the distinctness of the 
corresponding wholes and hence the separateness of knowledge 








TRUTH AND FALSITY 195 


and reality. The “‘systematic coherence” which is, on this view, 
at once Truth and Reality transcends the consistency of formal 
logic and ordinary thought. Thus there can be no separable 
truths, for such truths would not be the whole Truth. Though 
reality as thus conceived may be identical with thought as thus 
conceived, the limited reality of perceptual objects cannot be 
identified with the thought which is embodied in propositions or 
symbolic expressions, for if this were so there would be no fal- 
sity; every concept would refer toa real object. Since concepts 
and objects, in this less extended sense, are not identical but 
are distinct, the relation of concepts to objects, even when 
they come together in perception so that the meaning of the 
concept cannot be distinguished from the object, must be cor- 
respondence. This correspondence is a correlation such that the 
elements of the corresponding wholes fulfil the same structural 
functions in each; the relation of correspondence rests on an 
identity of logical form in real objects and in propositions or 
concepts. 

Truths are known only through belief or judgment, which is a 
secondary attitude toward propositions. This attitude is like 
understanding in that it is a preparation for an object intended, 
but it differs from understanding in being a completer prepara- 
tion — a willingness to act as if the object intended were in ex- 
istence. Belief is more than the thought of the existence of the 
object meant, and more than vividness of presentation or clear- 
ness of understanding. Belief, like meaning, is carried in sym- 
bols, it is inseparable from its expressions; and if there is any 
difference between belief and assertion, it is that the latter is an 
outward or inward signification of belief, while the belief itself 
is the attitude of mind signified. A full sentence differs from a 
single word or phrase in that it contains a sign of belief; the es- 
sential office of the copula is to serve as such a sign. But a word 
or phrase is no less capable of being true or false, and of being 


196 SYMBOLISM AND TRUTH 


asserted or denied, than a full sentence; a single word is a propo- 
sition. 

Disbelief reduces to belief, to a belief in the negative of the 
proposition disbelieved, while the true opposite of belief is in- 
credulity, the attitude of the sceptic. Disbelief is therefore posi- 
tive and takes a place beside belief as a means of reaching con- 
clusions through inference or through action; incredulity serves 
only the negative end of preventing error. 

Finally, the indecision of scepticism, which springs from the 
fact that truth is reached in no other way than through belief, 
can be escaped only by taking the risk of error which judg- 
ment necessarily involves; and belief, once it is set in motion, is 
carried on by its own momentum toward a theory of truth and 
reality — and in the end to “first philosophy.” For nowhere 
else are to be found the principles that justify all others. 








CHAPTER VI 


NEGATION AND CONTRADICTION 


I 


T xx notion of a negative truth — or a true negative — has an 
intrinsic appearance of paradox and even of self-contradiction, 
especially when truth is defined as the correspondence of propo- 
sitions, or symbolic expressions, with objects. 

What sort of object can a true negative mean? Does it stand 
for a “negative object”’? Clearly it must stand for some object. 
The significance of a negative cannot be, like that of a false prop- 
osition, a meaning determined by other meanings and yet corre- 
sponding to no object, for all negatives would then be false. Nor 
can it be a direct reference to objects given in perception. There 
are no negative data; perception is always the perception of 
something that is, never of something that 2s not. A direct refer- 
ence to objects cannot be anything but positive. The analysis of 
negation, therefore, falls between the horns of a dilemma: either 
negatives refer to no objects and are false, or they refer to ob- 
jects and are not negatives. 

There are many ways of escaping this dilemma, the simplest 
of which is to embrace one of its alternatives; and this is what 
Mr. Bertrand Russell does. He finds that negative propositions 
mean “negative facts,” which are unanalyzed and necessary 
elements in the world of fact." 

A negative fact, if there is such a thing, is plainly not of the 
same order as a positive fact. To observe that “the sun is not 
shining” is very different from observing the contrary. In the 


1 See B. Russell, “The Philosophy of Logical Atomism,” in The Monist, 
vol. xxviii (1918), and vol. xxix (1919). 


198 SYMBOLISM AND TRUTH 


latter case, a complex object, the shining of the sun, is immedi- 
ately given; in the former, what is immediately given is some- 
thing other than what is referred to. To “perceive” that the sun 
is not shining is to notice clouds in the sky and, perhaps, rain; 
or it may be, to observe that night has fallen — and these data 
are not negative facts. If negative facts are “given,” they are 
not given through perception, as are positive ones; they are in- 
ferred or constructed from perceptions; their reality, like that of 
classes, extends far beyond any immediate presentation; they 
are facts of a highly complex type, and the propriety of using 
the term “fact” for them is questionable, as it is for classes, 
which cannot properly be called “facts.” ? 

The assumption of negative facts as the referents of true nega- 
tive propositions does not analyze negation. It cuts the knot but 
leaves the threads of the difficulty tangled. Negative significance 
remains an anomaly unassimilated to the rest of knowledge, un- 
less it can be shown to have a positive basis in some other sort of 
meaning. | 

A particularly interesting attack on the problem is that of Mr. 
Raphael Demos, who, though he does not carry the analysis to 
its completion, suggests that a negative proposition is like a de- 
scriptive phrase; it is an ambiguous reference to what is meant 
by a number of positive propositions, the meaning of some one of 
which is the meaning of the negation.? Thus the sign of nega- 
tion, “not” or its equivalent, plays a part similar to that of the 
signs “‘a,” “any,” “some,” and “the.” It is a sign of interpre- 
tation. It does not signify a constituent of the fact to which the 
expression as a whole might refer, but indicates that the propo- 
sition is to be interpreted in a special way, that is, negatively ; 

1 See above, ch. IV, sec. xiii. 

2 See R. Demos, “A Discussion of a Certain Type of Negative Proposi- 
tion,” Mind, N.S., vol. xxvi (1917), p. 188. Despite obvious disagreements, the 


central idea of the theory of negation here presented, that of the ambiguity of 
the negative, is taken from Dr. Demos’ article. 





NEGATION AND CONTRADICTION 199 


which is to interpret it as a variable with an ambiguous refer- 
ence to certain positive propositions. 


II 


The ambiguity of negative propositions is their most striking 
characteristic. They are variables, and they continue as nega- 
tions only so long as their significance is not fully determined. 

If I assert that “the sun is not shining,”’ I do not assert that 
“it is raining,” or that “it is night,” or “that the sky is clouded.” 
None of these propositions expresses the meaning of the nega- 
tion. Nor do I assert all of these propositions. The meaning is 
like that of the statement, “I met a man.” If a value for the 
variable a man is chosen, so that the statement becomes, “‘I met 
Mr. X,”’ this is not what I assert; it is more specific than my 
actual assertion. And though I must have met Mr. X or Mr. Y 
or Mr. Z, etc., if the statement is true, still it remains undeter- 
mined which one of these men I did meet, and this indetermi- 
nateness is an essential element in the meaning. Similarly, what 
I mean by “‘the sun is not shining” might be either that “‘it is 
raining,” or that “‘it is night,” or that “the sun is in eclipse,” 
etc., but it is actually none of these. The negation is essentially 
unspecific in reference and to make it specific is to rob it of its 
negativity. 

The observation that negatives are ambiguous is the first step 
toward freeing us from the error that a negative is merely what 
zs meant. The manner of significance is no less constitutive of the 
meaning of a negation than are the things it might signify; and 
since propositions alone are ambiguous, negation belongs to the 
realm of propositions or concepts, and not to things. Things do 
not have negatives, for things are not ambiguous; and without 
ambiguity there is no negation. 

Toward what objects or facts is this ambiguous reference of 
the negative directed? 


200 SYMBOLISM AND TRUTH 


Every negation has its ground; it rests on a perception or af- 
firmation of fact. But the ground of a negation is not coexten- 
sive with the meaning, since the ground is a single fact or com- 
plex of facts, while the meaning covers a multitude of facts, 
some undetermined one of which is the value of the negative. 
I may affirm that “Chaucer’s Canterbury Tales are not good 
reading” on the ground that they are immoral, but this fact will 
not be the only possible interpretation of the statement. This 
negation might mean that the language of these tales is difficult, 
or that they are dull. If I advise you that “carbolic acid should 
not be drunk,”’ the ground of my advice may be that it is poison- 
ous; yet this is not what I assert, and you may construe my 
statement to mean that “suicide is criminal”’ or that “life is 
worth living.” To identify the ground of a negation with the 
meaning is to abolish the negation, for it is to choose one among 
the possible values; hence the negation is no longer a variable 
and no longer a negation. If a negative proposition were equiva- 
lent in meaning to the single positive proposition that is its 
ground, there would be no reason for employing negatives; they 
would disappear. Though negatives are often used where posi- 
tive propositions would serve as well, their function in knowl- 
edge is the same as that of other ambiguous expressions; 
namely, to avoid a definite reference or to refer to that which is 
not determinately known. Negation is notoriously the language 
of diplomacy and guile. 

In addition to the actual ground of any negation, there are 
many possible grounds. These possible grounds are all the prop- 
ositions with which the proposition negated is incompatible; 1 
and Mr. Demos limits the possible values of a negative to its 
possible grounds. On his view, then, a negative proposition 
means (ambiguously) the same as some one of the propositions 


1 Incompatibility is the relation of inconsistency between propositions, dis- 
cussed in chapter v. p and gq are incompatible if, when the one is true, the 
other is never true. This does not preclude both being false. 





NEGATION AND CONTRADICTION 201 


whose truth excludes the truth of the proposition negated. To 
say that “‘life is not short, nasty, mean, and brutish” is to refer 
to the fact that “it is long or happy,” or that “‘it is romantic,” 
or that “‘it is capable of perfection,” etc., none of these possi- 
bilities, however, being chosen as the value of the negative. 
Mr. Demos’s analysis does not go far enough. The relation of 
incompatibility or logical opposition, in terms of which it is 
stated, is complex; it rests on truth and falsity and is an extrin- 
sic rather than an intrinsic relation between concepts. It cannot 
be apprehended through direct inspection of propositions or con- 
cepts; one must know more than the meaning of a proposition to 
know that it is incompatible with another; he must know that 
it is never true when the other is true. Nor can incompatibility 
be apprehended as a relation between the data of perception. 
Logical opposition is not perceived, for what is meant by the 
logical opposites cannot be in the same universe; and if percep- 
tions seem to be inconsistent with one another, the inconsistency 
is in the concepts through which the data are presented, and not 
in the data themselves. The proposition “‘a is black”’ is incom- 
patible with the proposition “‘a is white,” “‘ Juliet loved Romeo”’ 
is incompatible with “Juliet hated Romeo’’; but white is not 
logically opposed to black, and love is not logically opposed to 
hate, since all of these qualities or relations exist in the same 
universe. Propositions alone can be logically opposed, and their 
logical opposition is a function of their truth and falsity. 
From the point of view of formal logic, there could be no ob- 
jection to defining “‘incompatibility ” in terms of truth and fal- 
sity and to deriving negation from this propositional relation. 
Nor could there be any objection to assuming incompatibility 
itself, without definition, as the foundation of a theory of nega- 
tion and truth. It is also possible to construct a logical system in 
which negation and incompatibility are both defined in terms 
of another function of propositions. Mr. H. M. Sheffer’s rejec- 


202 SYMBOLISM AND TRUTH 


tion is a primitive idea which makes these latter definitions 
possible." 

But what is primitive in a set of postulates for logic may be 
complex as an element in knowledge. The data of epistemology 
and the primitive ideas of logical systems are not simple in the 
same sense. For formal logic, the simplest primitive ideas for 
any system are those which are the smallest in number and 
which yield by deduction all the propositions belonging to the 
system; thus a number of different concepts might be chosen as 
primitive for different sets of postulates which apply, neverthe- 
less, to the same subject-matter. The facts to which these prim- 
itive ideas refer might have the appearance of extreme complex- 
ity, but this would not make the ideas any the less primitive and 
simple, so far as the logical part they play in the system is con- 
cerned. This is not the sense in which the basic ideas of a theory 
of knowledge are simple; these ideas are not arbitrarily chosen 
because of their economy and fruitfullness in deduction. Their 
simplicity must correspond to a certain simplicity in the subject- 
matter; what they mean must present the appearance of sim- 
plicity, it must appeal to the mind as being capable of no fur- 
ther analysis. It is this sort of simplicity which is lacking both in 
the concept of negative facts and in that of incompatibility as 
the basis of negation. 

It is possible to dissociate negation from truth and falsity, and 
thus to gain in completeness of analysis. The incompatibility or 
logical opposition of a negative and its positive is not the most 
fundamental idea involved in negation; this notion of incompat- 
ibility arises from a combination of the idea of truth with that of 
negation in a highly general sense. In order to understand a posi- 
tive proposition or symbolic expression, it is not necessary to 
consider whether it is true or false. (The only symbols whose 


1 H. M. Sheffer, A Set of Independent Postulates for Boolean Algebras, 
Transc. Amer. Math. Soc., vol. xiv, no. 4, pp. 481-488. 


NEGATION AND CONTRADICTION 203 


significance involves their truth are the elementary simple sym- 
bols from which complex expressions are constructed.) It is suf- 
ficient to know the form of the proposition and the meanings of 
its elements. The understanding of a negative, similarly, ought 
not to require a knowledge of its truth or falsity, or — what 
amounts to the same thing — of its incompatibility with an- 
other proposition. A negative must be such that it can be enter- 
tained as a possibility for thought without any consideration 
whatsoever of any object that it might mean, or that any other 
proposition might mean. Some relation which can be directly 
apprehended in apprehending the significance of propositions 
must be sought to mark the limits of the possible values of nega- 
tive expressions. This will yield the more general negation which 
does not depend on truth and falsity. 


Il 


This relation is that of distinctness of meaning; and it is the 
symbolic counterpart of the diversity or otherness of objects. A 
negative proposition means “something distinct from that 
which is meant by the positive’’; and this, coupled with the am- 
biguity of the reference, is the whole of negation when the ques- 
tion of the truth or falsity of the negative does not enter — that 
is, when the negative is purely a possibility for thought. 

This definition of the possible values of a negative proposition 
seems to remove all limitations and to lead to startling conclu- 
sions. Among the possible values of “‘the sun is not shining”’ are 
thus included, not only propositions that might be the ground of 
this negation, such as “it is night”’ and “‘the sky is overcast,”’ 
but also propositions that could by no stretch of the imagination 
be its ground — propositions such as “Chicago is in Illinois,” 


> 


‘‘man is a rational creature, ” etc. In short, any proposition 
which is distinct in meaning from “‘the sun is shining”’ is a pos- 


sible interpretation of “‘the sun is not shining.” 


204 SYMBOLISM AND TRUTH 


The appearance of paradox is partly removed if it is remem- 
bered that the negative proposition does not actually mean one 
of its possible values. It is a negative only while it is ambiguous; 
and, though some propositions are relevant to it as grounds from 
which its truth or falsity might be inferred, it no more signifies a 
particular one of these than it does a particular one of the count- 
less propositions irrelevant to it as grounds. The statement SiLite 
sun is not shining” does not actually mean “Chicago is in Tlli- 
nois,” nor does it mean ‘“‘the sky is overcast.’ It means “‘some- 
thing other than that the sun is shining.” If a pessimist were 
asked whether life is good, he might reply, “anything but”; and 
this inelegant, yet emphatic denial correctly indicates the range 
of possible values of a negative. 

It must be observed that the limit of the possible values of a 
negative is marked, not by the diversity of objects signified, 
but by diversity of significance, irrespective of objects. On this 
widest interpretation of the principle of negation, false propo- 
sitions (which correspond to no objects) may be values of the 
negatives of false propositions. “New York is not in Brazil” 
need not signify merely what is meant by some true proposition; 
it might mean (though being ambiguous it does not actually 
mean) that “New York is in Turkey.” And if I say that “Cin- 
derella did not love her stepmother,” which is false because 
there was no Cinderella, still I might mean that “Cinderella 
hated her stepmother,” which is also false. The question 
whether or not the truth of a negative precludes the truth of its 
positive is irrelevant to this purely conceptual negation. 

Any use of symbols presupposes distinctness as well as iden- 
tity of meaning. Thought is not a repeated series of tautologies, 
and no symbolic system could be constructed from symbols 
whose meanings were all equivalent. Just as every symbol, if it 
is to retain its identity (to be the same symbol) in its recurrent 
instances, must be interpreted in one and only one way, so a 








NEGATION AND CONTRADICTION 205 


symbol, if it is to have anything other than a reference so vague 
that it could not be called a meaning, must be distinct in sig- 
nificance from some other symbol; and where distinctness of 
meaning is present, negation is also present. The dictum that 
“determination is negation” is no less true for thought than for 
reality. Without negation, that is, without distinctness of mean- 
ing, there is no meaning; and without diversity there are no ob- 
jects. Everything that zs 1 is diverse from something else, and 
every significant idea is distinct in meaning from some other 
idea. Just as the same symbol or concept, when it is applied to 
the world of objects, will (by the very definition of the same 
symbol) mean one and only one object, so a symbol that is dis- 
tinct from it will (by the very definition of a distinct symbol) 
mean a different object or no object. And the negative, since 
it has the same significance as any symbol distinct from the 
positive, will therefore always be distinct in meaning from the 
positive. 


IV 


This general condition of the use of symbols — that a nega- 
tive is always distinct in meaning from its positive — which fol- 
lows from the purely conceptual definition of the meaning of a 
negative, is the principle of contradiction in its most abstract 
form. It is like the principle of identity in that it is a general rule 
of symbolism, and therefore a general principle of thought. 

Now the law of contradiction is often confused with the law of 
the excluded middle, which states that “either p or not-p is 
true”’; but this latter principle has no connection with the prin- 
ciple of contradiction, when truth and falsity are not considered 
in the definition of negation. As a general rule of symbolism the 
law of contradiction asserts that to every symbol corresponds 
another, its negative, whose meaning is distinct from the first. 


1 In the sense of ch. V. 


206 SYMBOLISM AND TRUTH 


It can be written, “‘a ¥ not-a,” the sign (#) being taken to 
mean “distinct from.’ Both the laws of identity and contradic- 
tion, on their purely symbolic interpretations, state general in- 
tentions in the use of symbols. The law of identity, “a = a,” 
tells us that any symbol “a” is equivalent, for symbolic pur- 
poses, to itself; that it can replace itself in any context without 
altering the meaning, since every symbol can have one and only 
one meaning. The law of contradiction, on the other hand, tells 
us that there is at least one symbol that is distinct, for symbolic 
purposes, from any given symbol “a,” and this is “not-a”’; if it 
replaces ‘“‘a’’ in any context, the meaning will be completely 
altered. 

As statements of general intentions in the use of symbols, the 
laws of identity and contradiction are a prior? in the sense that 
they are rules laid down by the mind for its own guidance. They 
are self-affirming; if they are denied, they are assumed, for no 
proposition or concept can be framed without them. In knowing 
what it is to think, we know these laws, and we can escape them 
only by escaping from the use of propositions or concepts — that 
is, from the use of symbols. 

There is another interpretation of these principles, an extsten- 
tial interpretation, which construes them as general truths about 
objects, as well as general principles of symbolism. If ‘‘a” stands 
for an object — for any object — “a = a” asserts that “any 
object is identical with itself,” or simply that “any object has an 
identity”; while “a # not-a” asserts that “any object is dis- 
tinct from anything other than itself,” or simply that “any ob- 
ject stands in the relation of diversity to-something.”’ Both of 
these statements are tautologies, but they could not be true un- 
less there were identity and diversity in the world of fact. They 
express the minimal conditions of the being of objects — that is, 
of the objects which are presented or represented in empirical- 
rational knowledge. 





NEGATION AND CONTRADICTION 207 


The very assertion of these general truths, however, assumes 
the laws of identity and contradiction as principles of symbo- 
lism. Only if “a” is the same symbol as ‘“‘a” does “a = a” 
affirm that “‘any object is identical with itself”; and unless “a” 
and ‘‘not-a” are always distinct in meaning, “a ¥ not-a”’ 
might mean “‘a # a.” The predication of diversity in objects 
presupposes diversity in the meanings of symbols, apart from 
objects meant, but the statement that “‘a # not-a” in the sym- 
bolic sense does not imply that a or not-a stands for an object. 
Though it is false to say that “griffins are not not-griffins,” if 
this means that griffins exist as distinct things, this is not false 
as a statement of how the concepts “griffin” and “not-griffin” 
are to be used. 

If the law of contradiction were not valid both on its symbolic 
and existential interpretation — if there were no distinct sym- 
bols and no diverse objects — thought would find itself in a 
strange situation. It would be impossible to think of anything 
without at the same time thinking of everything. In order that a 
symbol may mean a specific object, not only must the object be 
self-identical and the symbol be the same symbol in its different 
instances, but there must be something that is not meant by 
this symbol and that can be signified only through a different 


symbol — something for the apprehension of which a new and 


distinct concept is the only appropriate instrument. Without 


negation thought would be even less definite than the Parme- 


nidean tautology, “Being is”; and without diversity in objects, 
the whole structure of the world of fact, as we know it, would 
disappear. 

The limiting condition of the reality that gives truth, as we 
have defined it, to symbolic expressions or propositions is that it 
must be capable of being consistently presented and represented; 
and, so, for this reality, the principles of identity and contradic- 
tion on their existential as well as their symbolic interpretations 


208 ’ SYMBOLISM AND TRUTH 


must be true a priori. Anything that could be consistently pre- 
sented or represented would necessarily be self-identical and 
diverse from other things. The principles of identity and contra- 
diction are the “formal” categories of this limited being; the 
test of consistency, which makes use of the “empirical catego- 
ries”? of science and common sense, can be applied to existent 
objects only if these more general principles hold of them. 
These principles are implicit in the condition that marks the 
limits of this reality. 

How much further the validity of the laws of identity and 
contradiction, as truths about reality, can be extended is a 
matter for speculation; and here again the theory of knowledge 
finds its completion in metaphysics. If reality were constituted 
by thought, these most general conditions of thought would 
certainly be the most general conditions of being. But for a the- 
ory any less extended than this, it is a wide leap from the most 
general rules of thought to the most general principles of being. 
It is possible that reality cannot be trimmed to the neat dimen- 
sions of thought; there may be nooks and corners of the real 
hidden from this knowledge which demands the identity and di- 
versity of its objects. It is even possible that these very require- 
ments of thought form a barrier between the mind and reality, 
confining knowledge to a realm of Kantian phenomena. But 
neither this metaphysical alternative, nor the other — that they 
are true a priori of reality in the most inclusive sense of the 
term — can be established on the premises so far laid down. 


V 


What of the third “law of thought,” the principle of the ex- 
cluded middle? 

To construe the meaning of a negative proposition as “any- 
thing other than the meaning of the positive” appears to be a 
direct violation of this law, for this permits a false proposition to 


NEGATION AND CONTRADICTION 209 


be a value of the negative of a false proposition and therefore 
allows the possibility that when p is false not-p might also be 
false. “Paris is not the principal city of England” might mean 
“Paris is the capital of the United States,” and this is clearly 
not allowable if the principle of the excluded middle is true. 
Moreover, “‘Paris is not the principal city of England”’ could 
mean (though on account of its ambiguity it does not actually 
mean) that “birds have wings” or that “to-day is Friday,” and 
the truth or falsity of these propositions seems to be totally un- 
connected with the truth or falsity of ‘‘ Paris is the principal city 
of England.” 

The law of the excluded middle, that “either p or not-p (but 
not both) is true,” connects negation with truth and falsity by 
adding a further condition than diversity of meaning to deter- 
mine the possible values of a negative. We thus return to the 
more complex and special type of negation, which Mr. Demos 
defined in terms of incompatibility. This law is not a necessity of 
thought in the same sense as are the principles of identity and 
contradiction in their most general forms. The latter are needed 
if concepts or symbolic expressions are employed in any way 
whatsoever; the former enters only when truth and falsity (as 
well as the identity and distinctness of concepts) are considered. 
It is necessary for inference — for the derivation of the truth or 
falsity of propositions from the truth or falsity of others; but it 
is not necessary for the very existence of meaning, as are the 
first two laws of thought. 

In order that the principle of contradiction may yield the law 
of the excluded middle, the negative must be interpreted in a 
special way, which takes account not only of the distinctness of 
concepts, but of their truth. 

Now true propositions are distinct through the objects they 
mean, as well as distinct in significance apart from these objects; 
but false propositions are not distinguished from one another 


210 SYMBOLISM AND TRUTH 


through objects meant, since they mean no objects. Moreover, 
any true proposition is distinct from any false proposition 
through an object meant, for the one means an object, while the 
other does not. This notion of “being distinct through an object 
meant”? supplies the necessary principle for determining the 
possible values of a negative, when the law of the excluded mid- 
dle is added to the laws of identity and contradiction. If not-p 
means (ambiguously) the same as any proposition that is dis- 
tinct from p through the distinctness of an object meant, it will 
follow that when p is true not-p is false, and vice versa, that when 
p is false not-p is true. 

To include the idea of an object meant, that is, of truth, in the 
definition of negation is to remove negation from the realm of 
the purely conceptual. It is no longer sufficient merely to know 
the meaning of a proposition — merely to consider it as a possi- 
bility for thought — in order to know the meaning of its nega- 
tive. One must also know whether it is true or false. But if this 
kind of negation is less simple than the other, it is more effective; 
negatives now become instruments of inference. All false prop- 
ositions fall together as indistinguishable through an object 
meant, though they still remain distinct as concepts; and hence 
the negative of a false proposition can mean only true proposi- 
tions. It will be true for any value that can be chosen for it, so 
that the truth of not-p can always be inferred from the falsity 
of p. “New York is not in Brazil” will not include among its 
possible interpretations, “New York is in Turkey” or “New 
York is in Australia,’ since these propositions are not distinct 
through an object meant from “‘New York is in Brazil.” Any 
possible value of “New York is not in Brazil’’ will be a true 
proposition. Among these possible values there will be one that 
is the most probable ground of this negation, viz., “New York 
is in the United States”; but it is not necessary to suppose that 
this value is the sole possible meaning of the negation in order to 


tml i a 





sir 
— 


NEGATION AND CONTRADICTION 211 


establish its truth. Any true proposition will be a possible value 
of this negative. 

On the other hand, if p is true — and if there is a single false 
proposition among all the propositions which can be formulated 
— then not-p will be false. For among the possible values of 
not-p will be included, not only all the true propositions that are 
distinct from p through an object meant, but also some false 
proposition; and since the negative is ambiguous, it might mean 
this false proposition. It cannot be true if there is a single possi- 
bility of falsity.1 Thus, since it is true that “carbolic acid is 
poisonous,” and since some false proposition can be stated — let 
us say the proposition that “carbolic acid is good to drink”? — 
the negative, “carbolic acid is not poisonous,”’ might mean that 
*“‘carbolic acid is good to drink.” This latter proposition, being 
false, is a possible value of the negative of the original true prop- 
osition, for any true proposition is distinguished from any false 
proposition by an object meant. And though the negative, “car- 
bolic acid is not poisonous,” might also mean countless other 
propositions, both true and false, it cannot be true so long as 
there is any possible interpretation for which it is false. Thus 
where the possible values of a negative are the meanings of those 
propositions which are distinct from the positive through an ob- 
ject meant, the falsity of a negative can always be inferred from 
the truth of its positive. 

It is clear that this more restricted type of negation — this 
inferential negation — eliminates possibilities which the wider 
and simpler form of negation permits. When the negative is con- 
strued in this narrower way, “fairies do not live on bread and 
meat”’ could not possibly mean “fairies live on dew and honey.” 
Its positive being false (since there are no fairies), this propo- 


1 The assumption that some false proposition can be formulated amounts 
to the assumption that there is falsity; and certainly a negative could not be 
false unless there were falsity. There must be some false proposition that it 
could mean. 


212 SYMBOLISM AND TRUTH 


sition must mean the same as some true proposition; it must be 
true. By the very definition of the meaning of the negative, we 
are no longer permitted to consider it as a mere possibility that 
‘fairies do not live on bread and meat”’; we are forced to infer 
its truth from the falsity of the proposition of which it is the 
negative. The principle of the excluded middle thus drags us 
down to earth from the world of pure speculation. 


VI 


The conditions of the truth and falsity of negatives have al- 
ready been mentioned in passing. A negative is false if there is a 
single false proposition among its possible values, and it is true 
only if all of its possible values are true propositions. This fol- 
lows from the ambiguity of the negative. Let us examine this 
idea more closely. 

Now the meaning of a proposition determines whether it is 
true or false, and if this meaning is not fully specified — that is, 
if the proposition might mean a number of different things, but 
actually does mean none of these — the truth of the proposition 
will depend on what it might mean, not on what it actually does 
mean; for it actually does mean no specified object. Thus an am- 
biguous proposition (or one which contains ambiguous constitu- 
ents) is not true in the same sense as an unambiguous proposi- 
tion. Its truth, like its meaning, is fixed by possible references to 
objects, rather than by an actual reference. It is “ambiguously 
true.”’ To be true in this sense is to be susceptible of many differ- 
ent interpretations, but not to be susceptible of a false interpreta- 
tion. Just as ambiguous meaning is an unspecified possibility of 
meaning, so ambiguous truth is an unspecified possibility of 
truth, rather than truth for a definite object or class of objects. 
And if among the possible determinations of such an ambiguous 
expression there is one for which it would be false — if there is 
a single possibility of falsity — the proposition fails of truth as 





NEGATION AND CONTRADICTION 213 


an ambiguous proposition, even if it might be true for some of 
its possible values. Though an ambiguous proposition, if it is 
asserted, need not be asserted for all of the things it might mean, 
its truth requires that it be capable of being true for all of these. 

Consider the statement, “‘I saw a friend on the street yester- 
day.” This is a particular proposition but, since it contains an 
ambiguous constituent, it does not assert that I saw a particular 
friend — Brown or Jones; nor does it assert that I saw ali my 
friends. I might have seen any one of them, and if among them 
I count, as did the poet Blake, a certain group of friendly spirits, 
or if some whom I call friends are not friends, the proposition 
might be false; and the mere possibility of falsity invalidates it 
as an ambiguous assertion. If the assertion is true — which 
means that all possibility of interpreting it as false is eliminated 
— any person that could be meant by the variable “a friend” 
must be a real person, and must be really a friend. 

A negative is “ambiguously true.” If it is asserted, it is not 
asserted for one of its possible values or for all of them; it is am- 
biguously asserted. And if it is true, it must be true for more 
than one or several possibilities; there must be no possibility for 
which it could be false. A true negative embraces the entire uni- 
verse of true propositions, but not one false proposition; while a 
false negative embraces a universe of true and false propositions 
—one true proposition, only, being excepted: the positive of this 
negative. If these conditions of the truth and falsity of negatives 
are born in mind, the remaining implications of the principle of 
the excluded middle are easily seen to be true; v2z., that when 
not-p is false, p is true; and when not-p is true, p: is false. 

Suppose that not-p is false. Then some proposition that could 
be a value of it, some proposition other than p, must be false. 


1 This principle, “either p or not-p is true (but not both),” implies that 
(1) if p is false, not-p is true, (2) if p is true, not-p is false — both of which have 
been demonstrated in the previous section — (3) if not-p is false, p is true, and 
(4) if not-p is true, p is false. 


214 SYMBOLISM AND TRUTH 


But if p is also false, p would not be distinguished ‘‘through an 
object meant”’ from this value of not-p; that is, not-p would not 
be the negative of p. And therefore p must be true. Thus, since 
it is false that “men do not desire pleasure,” it cannot also be 
false that ‘‘men do desire pleasure.” For, if this were the case, 
one of the possible values of the negative, “men do not desire 
pleasure”’ — let us say the false proposition “‘men desire pain” 
— would fail to be distinct from the positive, ““men desire pleas- 
ure,” through an object meant; so that “men do not desire 
pleasure”? would not be the negative of “‘men desire pleasure.” 
The very definition of the possible values of this negative de- 
mands that its positive be true when it is false. 

On the other hand, when nof-p is true, p must be false. For, 
not-p being true can mean only true propositions; and, since it is 
always possible to state some false proposition (since there is al- 
ways falsity), unless p were false when not-p is true, not-p would 
include this false proposition among its possible values, for this 
false proposition would be distinct from p through an object 
meant, if p were true. Therefore p must be false. It is true, for 
example, that “fortune is no respecter of persons”; but some 
false proposition, g, can be stated; and if it were also true that 
“fortune is a respecter of persons,” this latter proposition would 
be distinct from the false proposition, g, through an object 
meant, and q would be a possible value of its negative. The nega- 
tive might then be false. Thus it must be false that “fortune is 
a respecter of persons”’ if it is true that “fortune is no respecter 
of persons.” 

Where the negative means ambiguously the same as any prop- 
osition distinct from the positive through an object meant, the 
law of the excluded middle is therefore valid in all of its implica- 
tions. From the truth (or falsity) of p, the falsity (or truth) of 
not-p can always be inferred; and from the truth (or falsity) of 
not-p, the falsity (or truth) of p can always be inferred. 








NEGATION AND CONTRADICTION 215 


VII 


The examination of judgment led us to the conclusion that to 
disbelieve or deny a proposition is to believe or assert its nega- 
tive — belief, like understanding, being an attitude of prepara- 
tion for or anticipation of something meant. But if the meaning 
of a true negative might be that of any one of an entire universe 
of true propositions, what possible attitude of preparation or an- 
ticipation could be appropriate to it? To prepare for so many 
truths would be to prepare for — and to believe — no specific 
truth; so that the analysis of negation seems to have given nega- 
tives a basis in fact at the cost of rendering their significance so 
vague that they cannot be believed. 

And yet there is a kind of belief which is appropriate to nega- 
tive propositions in their total ambiguity — a belief that is di- 
rected toward no specific object or class of objects. Such a belief 
is an anticipation of anything at all other than what is denied; it 
is a general readiness to accept something or other — anything 
excepting the proposition disbelieved — as true. This is the 
frame of mind in which the atheist denies God; he is prepared to 
believe anything but that there is a God. And it is the attitude 
one takes toward propositions which are plainly self-contradic- 
tory or false. If you tell me that “triangles have four sides” or 
that “oxen fly in the air,” I shall probably reply that I can ac- 
cept anything but this. This kind of disbelief, however, though 
it has a positive content of a formal and indefinite sort, amounts 
to little more than turning the mind away from the proposition 
disbelieved. It is a bare (and often groundless) disbelief which 
hardly escapes scepticism and which, like the sceptical attitude, 
can never take the place of a positive judgment in knowledge. 

Negatives are rarely thus asserted or believed in the full ex- 
tent of their possible meanings. Ordinarily, values which are 
relevant as grounds to the falsity of the proposition disbelieved 


216 : SYMBOLISM AND TRUTH 


are selected from among the possible values, and on these belief 
centers. 

Now the ground of a negative — and of the assertion of the 
falsity of a proposition — is some proposition which is incom- 
patible with the proposition negated or with the proposition 
that is believed to be false. It is a proposition which is never 
true when the other is true. And this incompatibility is deter- 
mined by the “empirical categories” of science and common 
sense. Scientific theories and laws, and prescientific generaliza- 
tions, are the tests not only of the existence of objects and the 
truth of propositions, but also of the “non-existence of objects” 
and the falsity of propositions. A proposition is false — it stands 
for no object and is conveniently, if inaccurately, said to mean 
a “non-existent object’ —when it is inconsistent with the whole 
of knowledge. The mere failure to discover something in exist- 
ence that the proposition might mean, though it may be ground 
for denial, is no proof of the falsity of the proposition, and can 
lead only to the bare disbelief which is directed toward no spe- 
cific truth. 

The grounds of negative judgments thus fall into two classes: 
the failure of verification(which is really privation of ground), 
and the discovery of true propositions from which the falsity of 
the proposition denied can be inferred by the aid of the general- 
izations of science and common sense. In the first case, when I 
believe a proposition to be false, I can merely deny it by affirm- 
ing its negative in its full ambiguity. In the second case, my be- 
lief will be capable of some limitation; I can select as its special 
objects the truths from which the falsity of the proposition in 
question follows. I am not therefore always confined to the 
formal knowledge that ‘“‘anything other than what is denied is 
true,” in affirming the falsity of propositions, though this is all 
that the definition of the meaning of the negative can tell me. I 
can infer, through the laws which I have found to hold in experi- 








NEGATION AND CONTRADICTION 21%, 


ence, that certain propositions are true when the other is false, 
and I can direct my belief toward these propositions. These are 
the “‘most probable”’ values of the negative. If I assert that “no 
man defies the laws of society with impunity,” I most probably 
believe that “‘crime is always punished” or that “criminals are 
detected” or that “‘the social outcast is miserable,” any one of 
which could be the ground of this negative judgment. But since 
there are, in any case, many possible grounds of falsity,— many 
propositions which are incompatible with the one negated,— to 
believe a negative, even when a whole universe of truths is not 
considered, is to prepare for more than a single contingency. 
And yet it is to prepare for a contingency, to be ready to act as 
if some definite propositions were true; and thus disbelief be- 
comes as fully positive as it is capable of becoming. 

The fact that this more fully positive type of disbelief is di- 
rected toward specific ones among the possible values of the 
negative does not restrict the meaning of the negative to these 
values, that is, to its possible grounds. The negative does not 
cease to be an “infinite negative” (as the older logicians called 
it), which might mean the same as any one of an indefinite 
number of propositions; nor are the formal requisites of its 
truth — that it cannot be false for any possible interpretation 
— altered. 

Thus negative judgments are never wholly equivalent in effect 
to positive ones, for there is always a margin of possibility which 
is not covered by belief, even when the “most probable” values 
of the negative are selected as the objects of belief. The “‘infin- 
ity” of the negative allows for the totally unforeseen and unfore- 
seeable — for contingencies which none of the principles of sci- 
ence and common sense embrace. When one believes a negative, 
therefore, he can find in his belief a residuum of that general 
readiness for anything other than what is denied — a margin of 
“preparation for the wholly unexpected’? — which arises from 


218 SYMBOLISM AND TRUTH 


the ambiguity of the negative. Negative judgments, no matter 
what their grounds, remain evasive to the end; they commit one 
to much less than positive judgments. They do not completely 
attain to the solidity and certainty of positive judgments. 


Vill 


It must not be forgotten that ideas can be entertained apart 
from belief and disbelief, as possibilities for thought; that nega- 
tion can be dissociated from truth and falsity; and that there is 
a realm of the purely conceptual, where identities and distinc- 
tions of meaning alone are relevant. 

The fact that the laws of identity and contradiction (when 
truth is not a part of the definition of the negative) are general 
rules of symbolism and therefore of thought, irrespective of ob- 
jects which are or might be meant, makes it possible to distin- 
guish conceptual validity from truth, and formal consistency from 
existential consistency. A system is conceptually valid, whether 
or not it is true, if it does not violate these two principles of the 
use of concepts. This means that symbols which are originally 
taken as distinct — to be values of the negatives of one another 
— must continue to be treated as distinct, and that symbols 
originally taken as identical must continue to be treated as iden- 
tical. These conditions are sufficient to give the system formal 
consistency. Whether it is existentially consistent and true — 
that is, whether it contains no incompatible propositions — is 
another matter, but this will in no sense affect its formal con- 
sistency. The consistency of the system is a consistency of defi- 
nition only. 

This sort of formal consistency and conceptual validity be- 
longs to uninterpreted deductive systems and to the whole 
world of romance and fiction. The canons of the constructive 
imagination are the laws of identity and contradiction, where 
these laws are rules of symbolism and nothing more. 








NEGATION AND CONTRADICTION 219 


IX 


The present analysis of negation, beginning with Mr. Demos’s 
notion that a negative proposition means ambiguously the same 
as some positive proposition which is incompatible with the 
proposition negated, has separated the idea of negation from 
that of truth, thus distinguishing purely conceptual from infer- 
ential negation. The law of the excluded middle requires that 
the negative be construed in the latter sense, and the law of con- 
tradiction in its most general form, that it be construed in the 
former. 

The assumption of “‘negative facts”’ as the referents of true 
negative propositions does not analyze negation; nor does the 
theory that the negative means ambiguously some proposition 
incompatible with the positive carry the analysis to its comple- 
tion, for the notion of incompatibility is complex; and though 
incompatibility might be taken as simple for purposes of deduc- 
tive exposition, it is not simple as an element in knowledge. 
Incompatibility is a function of the truth and falsity of prop- 
ositions. Negatives are unquestionably ambiguous, but if the 
possible values of a negative are restricted to its possible 
grounds, that is, to those propositions whose truth excludes the 
truth of the positive, the meaning of a negative cannot be dis- 
sociated from its truth or falsity. 

A negative proposition, where the negative is interpreted in 
the simplest way, means (ambiguously) the same as any propo- 
sition distinct in meaning from the positive, and this distinct- 
ness of meaning need not be connected with diversity in objects 
meant, that is, with truth. Distinctness of meaning, apart from 
objects referred to, is a necessary presupposition of the use of 
symbols; and the principle of contradiction, “a # noft-a,” as a 
general rule of symbolism and hence as an a priori condition of 
thought, asserts that a negative is always distinct in significance 


220 SYMBOLISM AND TRUTH 


from its positive. This principle is codrdinate with the law of 
identity, “a = a,” which asserts that any symbol is equivalent 
(or identical) in meaning with itself. Both of these principles can 
be interpreted in another way, that is, as general conditions of 
the being of objects, and these existential interpretations assume 
the principles as rules of symbolism. If a means an object — any 
object — the law of identity states that “any object is identical 
with itself,’ and the law of contradiction that “any object is 
distinct from anything other than itself.’ These statements are 
true only if existing objects have the formal characters of iden- 
tity and diversity. For the limited reality which can be con- 
sistently presented and represented — for the existing objects 
of empirical-rational knowledge — these laws must hold; but 
whether they hold for all reality can be determined by nothing 
less than a complete metaphysical theory. 

The third law of thought, the principle of the excluded middle, 
joins the idea of truth to that of negation. This principle is not 
necessary to the very existence of meaning, as are the others, 
but it is necessary to inference. If the negative means the same 
as any proposition distinct from the positive through an object 
meant, it will always be true that “either p or nof-p is true (but 
not both).” 

To believe a negative in its full ambiguity is to be ready to 
accept “anything other than the positive,”’ which is disbelieved. 
This form of bare denial does not limit itself to the possible 
grounds of the falsity of the proposition disbelieved. More com- 
monly, denial and disbelief are directed toward values specially 
selected from among the possible values of the negative; that is, 
toward the values which might be grounds of the falsity of the 
proposition denied. These grounds are determined by the gener- 
alizations of science and common sense, which are the tests of 
the “non-existence of objects” and the falsity of propositions, 
as well as of the existence of objects and the truth of proposi- 





: 


NEGATION AND CONTRADICTION 221 


tions. But no negative judgment is wholly equivalent in effect 
to a positive one, since its ambiguity is never eliminated, and it 
might mean something other than it is believed to mean. 

The material consistency of the knowledge whose truth and 
falsity is tested by its compatibility or incompatibility with 
other portions of knowledge (accepted as true) can be contrasted 
with the formal consistency of conceptual systems which con- 
form to the principles of identity and contradiction, as general 
rules of symbolism, but are not affirmed to be either true or 
false. Conceptual validity and truth are distinct. It is possible to 
construct valid deductive systems which are completely unin- 
terpreted, in which the identity and distinctness of concepts (or 
symbols) and of logical forms alone are considered. Logical form 
can be isolated and studied in itself. This is the work of the 
purely formal deduction which, in Mr. Russell’s phrase, “‘does 
not know what it is talking about, or whether what it says is 
true.” 


CHAPTER VII 


FORMAL DEDUCTION 


I 


Format logic might be defined as “‘the science of pure form,” 
for it is interested in forms, and their connections, apart from 
any “‘matter” in which they might be exemplified. Since sym- 
bols in themselves embody logical forms, formal deductive sys- 
tems can be presented in uninterpreted symbols, they can be 
stated as if they referred to no objects; and logical form, thus 
dissociated from a “‘matter,”’ becomes a subject of study in itself. 

There are numerous sets of postulates for geometry, — both 
Euclidean and non-Euclidean, — for arithmetic and algebra, for 
serial order, and for logic itself, which attain — or nearly attain 
— this ideal of abstract statement, and it is these systems which 
best illustrate pure deduction. An examination of them makes it 
plain that formal deduction is concerned with nothing but forms 
and their relations. In order that the deductive connections in 
_ these systems may stand forth clearly, they are separated from 
the subject-matter and stated in terms of postulates, axioms, 
and theorems which might equally well apply to other subject- 
matters. Though these postulates, axioms, and theorems can be 
interpreted in many different ways, their form remains the same 
whatever objects they refer to — even if they refer to no ob- 
jects. Their form is independent of all interpretations. 

Such systems are hypothetical in the sense that they are 
purely conceptual and not asserted. They conform to the prin- 
ciples of the construction of concepts, that is, of the use of sym- 
bols, and are therefore possibilities for thought; but the question 
of their truth or falsity does not enter. If complete interpretations 





FORMAL DEDUCTION 223 


for them can be found, they will be ‘‘materially”’ consistent and 
true for these interpretations; the hypothetical connections be- 
tween the postulates, axioms, and theorems will become infer- 
ences; the theorems can be truly asserted as consequences of the 
postulates and axioms. But if they have no interpretations, or 
only incomplete interpretations, these systems will still be possi- 
bilities for thought — conceptually “valid” and “formally” 
consistent; and, from the point of view of formal logic, this is all 
that they need be. 

It is not possible to empty a set of postulates of all meaning, 
for it would then cease to be a set of postulates. An uninter- 
preted deductive system is not a collection of meaningless marks. 
It has its plan of syntax, its groups, its terms and symbols of 
unity; its meaning is syntactical; within a general framework 
of significance, the uninterpreted symbols become variables, 
which, though they do not actually refer to objects, could refer 
only to objects whose formal characteristics are those given in 
the symbolic groups of the system. The general scheme of sym- 
bolic structure determines the possible values of these variables. 

Some symbolic context is always necessary to a variable. Out- 
side a context, a variable is not a symbol (and not a variable); 
and though the context of the variable may include symbols of 
fixed significance, this context need be only a formal plan of 
grouping. If every element, excepting the form, of a symbolic 
expression is a variable, the expression will not lose its meaning. 
If only one factor in the meaning is determinate, viz., the form, 
this will be sufficient to give the expression significance as a 
whole — a significance that has reached the maximum of in- 
determinateness. It is then the use of variables in a general con- 
text of logical structure which makes the study of form in itself 
possible. 

The meaning of a formal deductive system is syntactical, and 
so the postulates of the system are a plan of syntax, which de- 


224 SYMBOLISM AND TRUTH 


termines what groups have significance in the system and how 
these groups can be derived from one another. The deductive 
connections appear as rules of substitution, by which one sym- 
bol (or group) can replace other symbols (or groups) and yield 
expressions which still have meaning. To state this plan of syn- 
tax, it is necessary to assume nothing but the general principles 
of symbolism and certain possibilities of substitution; these as- 
sumptions are sufficient to make the system a connected whole 
which embodies a number of different logical forms related (hy- 
pothetically) to one another as premises to conclusions. The 
structure alone is constant; all other elements in the meaning 
are variable. When the system is asserted for a definite (and 
complete) interpretation, these hypothetical connections be- 
come the premises and conclusions of inferences, and the propo- 
sitions that were assumed in their maximum generality, without 
interpretation, prove to be a deductive exposition of truths 
which hold for certain sets of objects. But when there is no 
interpretation, the system retains its syntactical meaning; 
through the conditions of significance imposed on it, it contin- 
ues to be a presentation of logical forms connected in certain 
ways; and this is all it originally purports to be. 

It is not strictly true that, in putting forward a formal deduc- 
tive system, “we do not know what we are talking about,” 
though there is no doubt, since all the elements of the system 
with the exception of the form are variable, that we need not 
know or care “whether what we say is true.” We are talking 
about logical forms, which are given in the very symbols through 
which we talk about them. We are mapping possible systems of 
concepts, as Columbus mapped the continent of which he dis- 
covered only the shore; but in this case it is not even necessary 
to know that there is a continent to be mapped; we need know 
only the principles of map-making to explore the world of possi- 
bilities. 





FORMAL DEDUCTION 225 


II 


The general principles of symbolism, that is, the most general 
conditions of the construction of concepts, have already been 
stated. They are (1) the principle of group significance, that the 
meaning of any group is a function of the meanings of its ele- 
ments and their grouping; (2) the general rule of “‘symbolic 
grammar,” that every significant group must contain both a 
symbol of unity and terms (or a term), and this rule demands 
that the symbols of unity be distinguished from the terms; (3) 
the principle of identity, that every symbol has one and only one 
meaning; and (4) the principle of contradiction, that thereis at 
least one symbol which is always distinct in meaning from any 
given symbol, that is, its negative, which means (ambiguously) 
the same as any symbol other than the positive; and this prin- 
ciple demands that there be distinctness as well as identity of 
meaning. 

Every symbolic system must be such that it could be inter- 
preted, even though it refers specifically to no objects; other- 
wise, it would not be a possibility for thought. The general prin- 
ciples of symbolism themselves are the conditions under which 
systems could be interpreted. From these principles, in the 
above order, it follows that any purely conceptual system must, 
first, be composed of groups which are taken to be significant as 
wholes. If the system contained no such groups, its symbolic 
elements would not be variables, but mere meaningless marks.! 
Thus there must be certain signs of syntax to indicate the struc- 
ture of the groups — their divisions into major and minor 
wholes, and the group relations between these wholes. 

Secondly, the symbols of unity must be distinguished from the 
terms; and when the system is interpreted, the former will stand 


1 Or else symbols with a determinate reference to objects, in which case the 
system would not be uninterpreted. 


226 SYMBOLISM AND TRUTH 


for relations, operations, or qualities in their rdéle as elements of 
unity in facts, while the latter will stand for individuals or for 
universals in their substantive réle. There are no objects which 
are not terms related or qualified or operated on in some way; 
hence, without this distinction between symbols of unity and 
terms, the system could not be interpreted and would not be a 
possibility for thought. 

Thirdly, every symbol must be identical in meaning with it- 
self, that is, the equation, a = a, must hold throughout the sys- 
tem; and this principle (the principle of identity) gives a rule of 
substitution which is valid in all systems, v2z., the rule that any 
symbol can be substituted for itself without altering the mean- 
ing of the group in which it is substituted. The concept of iden- 
tity makes it possible, moreover, to define symbols which are 
distinct in character as identical in meaning. Indeed, many of 
the symbolic elements of a conceptual system may enter the 
system only through being identical in meaning with the origi- 
nal groups of other elements, that is, many of the variables may 
gain their variable significance through definition alone. Such 
equivalent symbols can replace one another in any of the groups; 
this also is a rule of substitution which is valid in all systems. 

Fourthly, symbols originally taken as distinct in meaning 
must be construed as distinct throughout. None of the transfor- 
mations of the system can result in the use of distinct symbols 
as the same or equivalent. For this would violate the principle of 
contradiction, which asserts that any possible value of a nega- 
tive, that is, any symbol distinct from a given symbol, is always 
distinct from this symbol. And yet this principle permits the sub- 
stitution of distinct, as well as identical, symbols for one another, 
when the special rules of the system so provide. Though such 
substitutions of distinct symbols for one another will always 
result in alterations of meaning, this fact does not render such 
substitutions impossible, for distinct symbols do not become 





FORMAL DEDUCTION Q227 


identical in meaning by being substituted for one another. Iden- 
tity of meaning is more than a possibility of mutual substitu- 
tion.’ In fact, the more important transformations in any sys- 
tem are the ones which come about when the symbols in groups 
are replaced by other (distinct) symbols. Special rules of substi- 
tution, which hold only for the special systems in question, pro- 
vide for transformations of this type. 

A formal set of postulates will begin by assuming that certain 
symbolic groups, whose terms and symbols of unity have been 
distinguished, are significant, that is, that these groups have syn- 
tactical meaning apart from any objects they might represent. 
A set of postulates will also assume some special rules of substi- 
tution, in addition to the general rule that the same symbol or 
symbols of identical meaning can replace one another. It may 
further assume certain special identities of meaning, that is, 
special equivalences or definitions, which (when the system is 
interpreted) will represent identities in objects. With these as- 
sumptions, the set of postulates is a complete plan of syntax for 
a symbolic system. Any group or equation which can be derived 
from the original groups or equations by the rules of substitu- 
tion will be significant in the system, and combinations of sym- 
bols which cannot thus be derived will be nonsensical; they will 
have no meaning in this context. The plan marks the boundaries 
of an area of concepts; it separates what is conceivable or sig- 
nificant in terms of its own symbols from what is inconceivable 
or nonsensical in these terms; but it does not separate what is 
true from what is false. All of its propositions are “‘thinkable”’; 
whether they are true or false is another and an irrelevant ques- 
tion. Deduction in a system of this type is the manipulation of 
the symbols according to the rules. 


1 Symbols which are identical in meaning must, if they stand for objects, 
stand for the same object; while symbols which can be substituted for one an- 
other may stand for diverse objects, and must stand for diverse objects if they 
are distinct in meaning. 


228 SYMBOLISM AND TRUTH 


The process of formal deduction, divorced from a subject- 
matter and occupied only with logical forms and their connec- 
tions, is the derivation by substitution of significant symbolic 
groups of different elements and forms from other symbolic 
groups; and a formal deductive system is a set of uninterpreted 
symbolic complexes of many distinct forms and elements built 
up, by this process of substitution, from a few simple symbols 
and symbolic complexes. Where possibilities alone are consid- 
ered, deduction is an engrossing game played with symbols. The 
rules of the game are the general conditions of the use of sym- 
bols, together with the possibilities of manipulation opened up 
by these rules and by any other special rules which may be de- 
vised for special systems. 


III 


The study of a set of postulates — for geometry, algebra, 
logic, or any other field of knowledge — reveals the importance 
of the part which substitution plays in formal deduction. 
Logicians speak of substitution as an essential modus operandi 
or real operation in uninterpreted systems.! It is in fact the sole 
means of connecting the theorems with the postulates and 
axioms when these postulates and axioms are purely hypotheti- 
cal, that is, when their truth or falsity as premises and conclu- 
sions is not even considered. 

Sets of postulates rarely state their rules of substitution ex- 
plicitly, though they always make use of such rules. One of the 
simplest methods of providing for the manipulation through 
substitution of the symbols of a deductive system is that em- 
ployed by Mr. E. V. Huntington.? As the “base” of a set of 
postulates, he assumes a class, K, of elements, a, b, c, etc., and 


1 See C. I. Lewis, A Survey of Symbolic Logic (1918), pp. 353 ff.; also A. N. 
Whitehead, A Treatise on Universal Algebra (1898), Bk. I, ch. 1, “On the 
Nature of a Calculus.” 

? See E. V. Huntington, Sets of Independent Postulates for the Algebra of 
Logic, Transc. Amer. Math. Soe. (1904), v, 288-309. 





FORMAL DEDUCTION 229 


relations or operations, R, S, etc. Since the postulates hold for 
any element of K, the terms, a, b, c, etc., can be mutually substi- 
tuted for one another without rendering the postulates invalid. 
Thus, if (aRb) is postulated in the system, (aRc) and (bRc) will 
also be in the system, Further, if the group (aRb), is itself an 
element of the class, K, it can be substituted for a, b, or c (since 
it might be any element of K), giving the complex ((aRb) Rb), 
etc. And if the substitutions were carried forward — (aRb) re- 
placing a or 6 in this latter group, and so on — an infinity of 
complexes of different forms would be provided for by this sin- 
gle possibility of substitution. The result of assuming the class, 
K, as a “‘base”’ is then the same as if it were explicitly stated, in 
the beginning, that any of the simple symbols of the system can 
be mutually substituted for one another, and any of the original 
groups can be substituted for any of the simple symbols. 

In the Principia Mathematica, Messrs. Whitehead and Rus- 
sell make use of substitutions in most of their proofs, especially 
in those of the earlier propositions from which the later ones 
follow by implication; and they speak of this process as “notic- 
ing that (these propositions) are instances of general rules,” ! 
that is, of the primitive propositions given in the first section of 
their work. These substitutions are possible, in the symbolic 
system of the Principia Mathematica, because these primitive 
propositions are principles of logic asserted for any proposition, 
rather than purely uninterpreted groups of symbols. In Mr. 
Huntington’s language, the class, K, of the Principia Mathe- 
matica is the class of all propositions; any proposition can be 
substituted for any other in the original complexes of the sys- 
tem. For example, p v p->- p, states that ‘“‘any proposition or 
the same proposition implies itself.’’ And from this postulate, 
together with the definition of implication, p > g-=-~pvq, 
which asserts that “‘an implication between two propositions 

1 Whitehead and Russell, Principia Mathematica, i, 102. 


230 SYMBOLISM AND TRUTH 


means that either the first is false or the second true,” the princi- 
ple of reductio ad absurdum, p > ~p:+ >+~>p (“any proposition 
that implies its negative implies its own falsity”), can be de- 
rived by substitution as follows: The proposition, ~p, (not-p), 
is substituted for p in the primitive proposition, pv p:>:?p, 
giving ~pv op->+ op. Now, if wp is substituted for q in 
the definition of implication, the resultisp 3 ~p-=: pvp; 
and if p > ~p (being equivalent to ~pv ~p) is substituted 
for the latter in ~pv w~p:>5-~p, we have p > ~p->. op, 
the principle of reductio ad absurdum, which was to be proved. 
This proof illustrates how the Principia Mathematica derives the 
‘“‘immediate consequences of the primitive propositions.” “‘The 
recognition that a certain proposition is an instance of some gen- 
eral proposition previously proved or assumed,” say Messrs. 
Whitehead and Russell, “‘is essential to the process of deduction 
from general rules”’; ! and this is, in effect, the recognition that 
certain substitutions are permitted in the system. 

It must be observed that these deductive substitutions are al- 
ways carried through completely. If one symbol replaces an- 
other in a group, it replaces the latter wherever it occurs. Thus, 
when ~7 is substituted for p in pv p->->=, every instance of 
the symbol p becomes an instance of ~p, giving ~pV ~p+a- 
op. That the substitutions must be complete is a general prin- 
ciple of deductive substitutions, the reason for which is not im- 
mediately evident. 

It will be remembered that the distribution of tautologous 
(or recurrent) elements is a formal feature of symbolic groups. 
Now, if the rule of completeness of substitution were not followed, 
groups that include tautologous members could be transformed 
into groups in which no tautologous members were present. A 
reflexive group, such as (Raa), could yield a non-reflexive group, 
such as (Rab). There is no objection to this if the system in ques- 


1 Loe. cit. 





FORMAL DEDUCTION 231 


tion contains a non-reflexive group (which is otherwise the same 
in form) for every reflexive group.’ But if the system contains no 
non-reflexive groups (or only non-reflexive groups which do not 
correspond in other formal features with its reflexive groups), 
the rule of completeness of substitution will be needed; other- 
wise, complexes which have no significance in the system will be 
introduced. In the first type of system (one which contains a 
non-reflexive group corresponding to every reflexive group), it 
is always possible on the other hand to derive the reflexive from 
the non-reflexive groups by substituting instances of the same 
symbol for distinct symbols: (Rabe), for example, gives (Raaa) 
if a is substituted for both b and ¢, so that the rule of complete- 
ness of substitution can be imposed on these systems without 
decreasing their deductive possibilities. The rule is therefore 
assumed as a general principle, applicable alike to those systems 
for which it is necessary and to those for which it is redundant. 
The reason is, in short, that non-reflexive complexes are more 
general in form than reflexive ones. The rule of completeness of 
substitution prevents us from deriving the more general forms 
(the non-reflexive) from the less general (the reflexive), but per- 
mits us to derive the less general from the more general by sub- 
stituting instances of the same symbol for distinct symbols. 
Though this latter type of substitution — of instances of the 
same symbol for distinct symbols — is permitted by the rule of 
completeness of substitution, it is not required by this rule, and 
it cannot be assumed that in all systems instances of the same 
symbol can replace distinct symbols. If this were erected into 
a general principle, there would be no systems which did not 
include reflexive groups, and there are many such — notably, 
systems of serial order. Indeed, for some systems, it can be laid 
down as a special rule that distinct symbols must always be re- 


2 The term “reflexive group” is here taken in a general sense to mean any 
group containing tautologous members, however distributed. 


232 SYMBOLISM AND TRUTH 


placed by distinct symbols. In these systems it would be impos- 
sible to derive a complex such as (Raaa) from one such as (Rabe). 
This special rule prevents the introduction of tautologous ele- 
ments where tautologous elements were not originally present; 
it is applicable to systems whose complexes are irreflexive 
throughout. But if this narrower condition of substitution is not 
introduced, it is taken for granted that instances of the same 
symbol (that is, tautologous symbols) can replace distinct 
symbols; that reflexive groups can be derived from all the non- 
reflexive groups in the system. 

In most deductive systems, then, the rules of manipulation 
permit any of the original terms mutually to replace one an- 
other, and any of the basic or derived groups to replace any of 
these terms — the rule of completeness of substitution being al- 
ways observed, and the rule that distinct symbols must be sub- 
stituted for distinct symbols being sometimes added. 

Still other possibilities of manipulation than these highly gen- 
eral ones are usually provided for in a set of postulates. It may 
be specified that some of the groups are identical in meaning 
with others or with some of the original terms, and hence that 
these symbols of identical meaning can be mutually substituted 
for one another. In Mr. Huntington’s first set of postulates for 
the algebra of logic, among other equations, the following ap- 
pears: a® (b@c) = (a@®b) @ (a@c). When the system is 
interpreted, this equation means “a or b and ¢ is identical with 
a or b and aor ec.” ? It represents different structures in an iden- 
tical object, that is, on the class interpretation of the algebra, 
the expressions on each side of the sign of equality stand for the 
same class. But when the system is uninterpreted, the equation 
merely states an intention to use these groups as identical in 


1 There are some systems, however, in which the basic or derived groups 
cannot be substituted for the original terms, and an example of such a system 
is given below. See below, sec. vii, note. 

? See E. V. Huntington, op. cit. 





FORMAL DEDUCTION 233 


meaning, whether or not they refer to objects. Since such as- 
sumed identities of meaning equate different logical forms, they 
are “equations of structure.” 

In lieu of or in addition to these equations of structure, a sys- 
tem may include connections of meaning which appear as impli- 
cations. It may be specifically provided that some of the groups 
imply others. For instance, in Mr. Huntington’s postulates for 
serial order, it is stated that (afb) (bRc) “implies” (aRc), and 
this asserts (where R stands for the relation “‘precedes”’) that “if 
a precedes b and b precedes c, a precedes c.”’ ! Now, in an unin- 
terpreted system, these cannot be implications of the usual sort, 
for ordinarily implications are functions of the truth values of 
the propositions they unite; p implies g means that “either p is 
false or q is true,” that is, that when p is true, q is also true. Truth 
values are not considered in an uninterpreted system, and so 
these implications cannot be truth-implications. They become 
truth-implications when the system is interpreted. Otherwise, 
they are connections of meaning apart from truth and falsity, 
and as such are nothing but possibilities of substitution. If p im- 
plies q in an uninterpreted system, this implication means sim- 
ply that q can replace p as a conclusion in any deduction. Any 
series of transformations that leads to =: leads also to q. 

These “implicational substitutions” belong to a special class, 
and must not be confused with the others. If q is an “implica- 
tional substitute” for p, this provision does not allow q to take 
the place of p in any complex in which p appears; but it does 
allow q to be substituted for p when p appears at the end of a 
chain of deductions. And this is readily verified by any concrete 
example of implication: “x is human” implies “x is mortal,” 
and if “‘x is human” is deduced from the fact that “x walks 
erect and speaks,” “‘x is mortal”’ can also be deduced from this 
fact. But “x is mortal” cannot replace “‘x is human” wherever 


1 E. V. Huntington, The Continuum (1917), p. 10. 


234 SYMBOLISM AND TRUTH 


the latter occurs; for instance, ‘zx is human” implies that “zx 
thinks’; and yet “x is mortal” does not imply that “x thinks.” 
An implicational substitute for any expression cannot replace 
this expression as a premise, or as a constituent in any expres- 
sion whatsoever, but it can replace it as a conclusion. 

There is one other important type of manipulation which 
must be noticed. The process of substitution is transitive, that 
is, if a can be substituted for b and 6 can be substituted for ¢, a 
can be substituted for c. If each of a series of propositions can 
replace one another in order, all of the intermediate steps can be 
dropped; the first of the series can be replaced by the last. This 
transitivity of substitutions enables us to bring together the 
premise and conclusion of a long line of deductions, the interven- 
ing links being omitted. And this principle applies where the 
substitutions proceed via identities of meaning, or where a con- 
clusion is replaced by something that it implies. Such condensa- 
tions of chains of deduction are employed in all systems; and the 
general rule that permits them will hereafter be used without 
specific statement, and will be referred to in proofs as “conden- 
sation.” 

The single modus operandi of pure deduction is the “real oper- 
ation” of substitution. By this operation alone the theorems of 
a deductive system are developed from the basic groups, equa- 
tions, and implications; and by this operation, also, the pre- 
mises and conclusions of the system are brought together or 
“condensed.”’ The postulates and theorems affirm no truths and 
no relations between truths. All that is considered is what groups 
have meaning in the system, and how these groups can replace 
one another. 

The manner of formulating a plan of syntax, that is, a set of 
postulates, for a deductive system, so that the basic groups can 
be transformed by substitutions into theorems, will be better 
understood through a more complete illustration, in which there 





FORMAL DEDUCTION 235 


are many different possibilities of symbolic manipulation. The 
substitutions will always follow (1) the rule of completeness and 
(2) the rule that the same symbol, or symbols of identical mean- 
ing, can replace one another; but the special condition, that dis- 
tinct symbols must be substituted for distinct symbols, will not 
be imposed. When this system is before us, we can ask what con- 
nections among facts the deductive manipulations of the sym- 
bols might represent. 


IV 


The system chosen as an illustration is a Boolean Algebra, an 
algebra of logic; and it will be interpreted as referring to classes 
and class relationships, though it can be interpreted in several 
other ways, e.g., in terms of regions in space together with cer- 
tain relations between these regions.! But no interpretation is 
necessary to it. Through symbolic complexes of variable ele- 
ments, which have syntactical meaning apart from objects they 
might mean, it presents an area of possible logical forms and 
shows how, from a few of these forms, all the others can be de- 
rived. Logical forms and their connections are its sole concern. 
It is complete in itself as a collection of symbolic groups, equa- 
tions, and rules of manipulation; and if it had no interpretation 
it would still be an experiment in possibilities for thought. That 
it happens to be a class algebra is an interesting and useful acci- 
dent, but not essential to it. 

(1) The basic groups of this system are (Rab), (Sab), and 
(Na). R, S, and N are undefined symbols of unity, and a and b 
are undefined terms. The parentheses are signs of syntax or 
grouping, to be construed in the way in which such signs are 
always construed. (Since these groups have a logical structure, 
they are significant, and the symbols R, S, N, a, and b are vari- 


1 See E. V. Huntington, op. cit. 


236 SYMBOLISM AND TRUTH 


ables.) A third undefined term, c, will also be assumed. R, S, N, 
a, b, and c are symbolically distinct.’ 

(2) The substitutions permitted are: (a) any of the undefined 
terms can be mutually substituted for one another, and (b) any 
of the basic symbolic groups, or any groups derived from them, 
can be substituted for any of the undefined terms. This latter 
rule permits substitutions in one direction only, that is, the un- 
defined terms cannot be substituted for any of the groups, un- 
less they are equivalent to them. (The rule of completeness of 
substitution, and the principle that the same or equivalent sym- 
bols can replace one another, are taken for granted.) 

(3) The following identities of meaning are assumed: 


A. Ra(Sb(Nb)) = a. C. Ra(Sbc) = S(Rab)(Rac). 
B. Sa(Rb(Nb)) = a. D. Sa(Rbe) = R(Sab)(Sac). 
Since the original undefined terms of the system appear on 
both sides of these identities, these identities are not definitions. 
When the system is interpreted, these equivalences will repre- 
sent differences of structure in an identical object. ? They are 
*“‘equations of structure.” 
(4) Two symbols which are not among the undefined terms 
are introduced by definitions: 
E. z = Sa(Na). F. u = Ra(Na). 


These are definitions because z and wu are not included in the 
original terms but enter the system only through being identical 
in meaning with certain ones of its significant groups. Such 
definitions are not necessary to the exposition; they are merely 
symbolic conveniences which condense complex expressions. 
But it would be uneconomical to take as undefined, and hence to 


1 The spatial order of the symbols in the groups is irrelevant; it plays no 
part in their logical form, which is determined by grouping alone; and there- 
fore it is not necessary to mention the fact that (Rab), (aRb), and (abR) are 
the same symbol. 

2 See above, ch. II, sec. vi. 





. 
1 
; 
’ 
‘ 
{ 


FORMAL DEDUCTION 237 


place among the original (primitive) symbols of the system, a 
symbol whose meaning could be defined through some of the 
groups. “Occam’s razor”’ must always be applied; entities must 
not be assumed unless they are necessary. (It is to be noted that 
the rules of substitution given in (2) hold for the original terms, 
and not for z and wu. There are special rules for these terms, which 
can be deduced from the other rules.) 

The general and special conditions of substitution permit 
three classes of transformations in this system: (1) The elements 
of a group can be altered without altering its form. If, for ex- 
ample, a replaces b, and ¢ replaces a, in Ra(Sb(Nb)) = a, this 
substitution will give the equation, Re(Sa(Na)) = c, which is of 
the same form as the first, but of different elements. Such trans- 
formations are unimportant. (2) Tautologies can be introduced 
where tautologies did not originally appear, for there is no pro- 
viso that distinct symbols must be replaced by distinct symbols. 
Thus from Ra(Sb(Nb)) = a, we can derive Ra(Sa(Na)) = a; 
from (Rab) or (Sab) we can derive (Raa) or (Saa), etc. The sys- 
tem therefore contains reflexive forms corresponding to all its 
non-reflexive forms. (3) Complexes of a higher type can be de- 
rived from complexes of a lower type, and this process can be 
carried, theoretically, to infinity. (Rab), for example, yields 
(Ra(Rab)), and this complex yields (Ra(Ra(Rab))), etc., when 
(Rab) is substituted for b; so that the system contains an infinity 
of possible forms. 

It is apparent that all of the complexes which appear in the 
equations, A, B, C, and D, and in the definitions, E and F, are 
significant in the system; they can all be derived from the basic 
groups by these rules of substitution. 

The “equations of structure”’ and the definitions, moreover, 
make possible a fourth class of transformations, those obtained 
by substituting equivalent symbols or groups in groups. With- 
out the “equations of structure,” each of the groups in the sys- 


238 SYMBOLISM AND TRUTH 


tem might, when the whole is interpreted, stand for a distinct 
object. The equations impose limitations on these possible dis- 
tinctions of meaning, as do also all the other equations which 
can be deduced from them by proper substitutions; and at the 
same time these equations increase the number of manipula- 
tions which can be performed in the system. 

(5) Some of the most important theorems, and their deriva- 
tions, are the following: 


1. Raz = a. 2. Sau = a. 


The proof of these two theorems requires the definitions, E 
and F.. These definitions are, like the other equivalences in the 
system, subject to all the permitted transformations by substi- 
tution. Therefore, z = Sa(Na) yields z = Sb(Nb) by the sub- 
stitution of 6 for a; and u = Ra(Na) yields u = Rb(Nb), by a 
similar substitution. And, since equivalent symbols can be sub- 
stituted for one another, we can derive Raz = a from the equa- 
tion Ra(Sb(Nb)) = a by replacing Sb(Nb) by z. Similarly, we 
can derive Sau = a by replacing Rb(Nb) by u in the equation 
Sa(Rb(Nb)) = a. This is the deduction of theorems 1 and 2. 

The rules for the substitution of these two special symbols, z 
and u, follow from their definitions. Since they are equivalent, 
respectively, to Sa(Na) and Ra(Na), they can be substituted for 
any symbol for which these groups can be substituted. There- 
fore, they can replace any of the terms, a, b, c, ete., of the sys- 
tem; but these terms cannot replace them, for these terms can- 
not replace the groups through which z and wu are defined. In 
other words, so far as concerns the manipulation of the symbols 
in this system, z and u are values of any of the variable terms, 
but they are not themselves variables; they are constants.! 


1 This introduces a new kind of variability, “functional variability,” which 
is something other than indeterminateness of significance; z and wu are func- 
tional constants, rather than functional variables; but their meaning is still 
undetermined. This is explained below, sec. vi. 





FORMAL DEDUCTION 239 


Other theorems are the following: 


8. Raa =a 
Proof: 
a = Sau (by theorem 2). 
Raa = Su(Raa) (Raa replaces a in 2.) 
Su(Raa) = S(Ra(Na)) (Raa) (By def. F, Ra(Na) replaces u). 


S(Ra(Na))(Raa) = Ra(Sa(Na)) (where a replaces b, and Na re- 
places c, in C). 


Ra(Sa(Na)) = Raz (By def. E, z replaces Sa(Na)). 
Raz =a (by theorem 1). 

Therefore: a = Raa (“‘condensation”’). 

4. Saa =a. 


This can be deduced in exactly the same manner as 3, by 
using theorem 1 for 2 and u for z. Theorems 3 and 4 are the 
analogues of one another for the symbols of unity R and S 


respectively. 
5. a = N(Na) 
Proof: 
1’. 2 = S(Na)(N(Na)) (by def. E, where Na replaces a). 
2’, u = R(Na)(N(Na)) (by def. F, where Na replaces a). 
a = Raz (by theorem 1). 
Raz = Ra(S(Na)(N(Na))) (By 1’, S(Na)(N(Na)), replaces z). 


Ra(S(Na)(N(Na))) = S(Ra(Na))(Ra(N(Na))) 
(by C, where Na replaces 6 and N(Na) replaces c). 
S(Ra(Na))(Ra(N(Na) = Su(Ra(N(Na))). 
(By def. F, u replaces Ra(Na)). 
Su(Ra(N(Na))) = Ra(N(Na)) (by theorem 2, where Ra(N(Na)) 


replaces a). 


Therefore: 3’. Ra(N(Na)) =a (“condensation”’). 
N(Na) = R(N(Na))z (by theorem 1, where N(Na) re- 
places a). 


R(N(Na))z = R(N(Na))(Sa(Na)). (By def. E, Sa(Na) replaces z). 
R(N(Na))(Sa(Na)) = S(R(N(Na))a)(R(N(Na))(Na)) 
(by C, where N(Na) replaces a, a replaces b, and Na replaces c). 
S(R(N(Na))a)(R(N(Na))(Na)) = S(R(N(Na))a)u 
(By 2’, u replaces the group R(N(Na))(Na)). 
S(R(N(Na))a)u = R(N(Na))a (by theorem 2, where R(N(Na))a 
replaces a). 
Therefore: 4’. N(Na) = R(N(Na))a_ (“condensation”). 
Therefore: N(Na) =a (by “‘condensation” of 3’ and 4’). 


240 SYMBOLISM AND TRUTH 


When the system is interpreted as a Boolean Algebra, this 
theorem is the principle of double negation. (It is to be noted in 
the proof that the group Ra(N(Na)) in 3’ is the same as the 
group R(N(Na))a in 4’, since the spatial order of the symbols is 
irrelevant.) 


6. 2=Nu 

Proof: 

z = Sa(Na) (by def. E). 

z= Su(Nu) (u replaces a in def. E). 

Su(Nu) = Nu (by theorem 2, where Nu replaces a). 
Therefore: z = Nu (“‘condensation”’). 
7. ui= Nz 

Proof: 

u = Ra(Na) (by def. F). 

u = Rz(Nz) (z replaces a in def. F). 

Rz(Nz) = Nz (by theorem 1, where Nz replaces a). 
Therefore: u = Nz (“‘condensation’’). 


Some of the other theorems which can be derived in the sys- 
tem, but of which the proofs are not given, are the following: 


8. Rau = u 12. Rab = N(S(Na)(Nb)) 
9. Saz =z 13. Sab = N(R(Na)(Nb)) 
10. Ra(Sab) =a 14. R(Rab)b = Ra(Rab) 
11. Sa(Rab) = a 15. S(Sab)b = Sa(Sab) 


The introduction by definition of the group (b(Za)) simplifies 
the system; on the class interpretation of the algebra this group 
means that the class a is included in, or “subsumed under,” the 
class 6.! This new complex can be defined in several different 


ways: 
(b(Ta)) =(Rab = b) (G) 
(b(Ia)) = (Sab = a) (H) 
(b(Ia)) = (Rb(Na) = u) (I) 
(b(Ia)) = (Sa(Nb) = z) (J) 


1 The grouping of (6(Ia)) indicates that it has a “‘sense”’ or order; the al- 
ternative order is (a(Ib)). No specific symbol of unity is inserted to join the 
sub-group (Ja) or (Ib), as the case may be, to the term a or b; the outer paren- 
theses show that they form a group, and this is all that is necessary; their 
group unity is of the most general sort — simply “‘togetherness”’ or “unity.” 





FORMAL DEDUCTION 241 


Some of the postulates and theorems stated above can be 
translated into the terms of this new group, and this translation 
will give, among others, the following theorems: 


16. (a(Iz)) 
Proof: 
(Rbz = b) is in the system (b replaces a in theorem 1). 
(Rab = b) = (b(Ia)) (by def. G). 
(Rzb = b) = (b(Iz)) (z replaces a in def. G). 


Therefore: (b(Iz)) is in the system, since it is equivalent by definition to a 
group in the system. 


17. (u(Ia)) 

Proof: 

(Rau = u) is in the system (by theorem 8). 

(Rab = b) = (b(Ia)) (by def. G). 

(Rau = u) = (u(Ia)) (u replaces 6 in def. G). 
Therefore: (u(Za)) is in the system. 
18. (u(Iz)) 

Proof: 

(Ruz = u) is in the system. (u replaces a in theorem 1). 

(Ruz = u) = (u(Iz)) (u replaces b, and z replaces a, in 


def. G). 
Therefore: (u(Iz)) is in the system. 


19. (a(I(Sab))) 
20. ((Rab)(Ia)) 


The proof of theorems 19 and 20 is similar to that of 16, 17, 
and 18, where theorems 10 and 11 and definitions G and H are 


employed. 
21. (a(Ia)) 
Proof: 
(Raa = a) is in the system (by theorem 8). 
(Raa = a) = (a(Ia)) (a replaces b in def, G). 


Therefore: (a(Ia)) is in the system. 


There are many more theorems in terms of the group (b(Ja)) 
which are not stated. 

This group is unlike the groups in terms of R, S, and N in that 
there are no rules which permit the substitution of (b(Ia)), or 


242 SYMBOLISM AND TRUTH 


its derivatives, for the original terms, a, b, and c, of the system. 
The group is defined as identical in meaning with the equiva- 
lence (Rab = b), or with the other equivalences given as H, I, 
and J. It can, therefore, be substituted for these equivalences; 
and when the latter, or their derivatives, are members of the 
system, some J-groups will also be, by definition, members of 
the system. But (Rab = 6), or the other equivalences, H, I, and 
J, cannot be substituted for a, b, and c; and hence the J-groups 
cannot be substituted for these terms.! 


V 


In practice, all deductive systems are devised with one eye on 
the facts, that is, on an interpretation. They are stated as if they 
referred to no objects, but they prove in the end to be connected 
expositions of truths which hold in some realm of experience, 
that is, to be systems of geometry, algebra, logic, etc. And if the 
plan of a system were constructed without this arriére pensée, it 
is not likely that an interpretation — or anything more than a 
trivial one — could be found for it. To explore all possibilities 
for thought, cut off from moorings in the world of the actual, 
would be an interesting but an endless experiment, for the num- 
ber of possible conceptual systems is infinite; and so those sys- 
tems which embody the structure of actual sets of objects are 
selected. Pure speculation then gives way to assertion, what 
seem to be arbitrary manipulations of symbols become infer- 
ences, and the significance of the whole is bound down to the 
real. A conceptual system which corresponded to no subject- 
matter would be an exercise in logical construction, and nothing 
more. Yet such exercises show that from the point of view of 


1 The original rule of manipulation, that any of the basic groups or their 
derivatives can replace any of the basic terms, does not provide that the 
“equations of structure”’ or the definitions, taken as wholes, can replace these 
terms; for these identities of meaning are not derived from the basic groups 
(though their constituents are), but are postulated on their own account. 





FORMAL DEDUCTION 243 


formal logic all that need. be considered, even in an interpreted 
system, are logical forms and their connections. 

The system which has been developed here is adapted to sev- 
eral different subject-matters. The symbols a, b, and c can stand 
for propositions, and the groups (Rab), (Sab), and (Na) for cer- 
tain “truth-functions”’ of propositions; v2z., (Rab) will mean the 
proposition, “either a or b (not excluding both) is true”; (Sab) 
will mean the proposition, “‘a and 6 are both true’; and (Na) 
will mean the negative of a. Another interpretation can be given 
in terms of regions of a plane surface, together with certain rela- 
tions between these regions; viz., (Rab) represents the region 
that includes both regions a and 6; (Sab) represents the region 
where a and b intersect; and (Na) represents all of the plane 
that lies outside the region a.1 We shall interpret the system as a 
logic of classes. 

A class has previously been described as a totality of distinct 
objects which have some predicate in common. Every predicate 
determines such a totality, e.g., the predicate “‘man”’ deter- 
mines the class ““men.”’ Classes may be related to one another in 
many ways, and these class relationships can be employed in 
reasoning. Classes may overlap, they may include or exclude onc 
another, their members may be added together to form a new 
class. There is also a null class, one that has no members, the 
class of “nothing”; and this class is determined by any predi- 
cates of which there are no instances, e.g., “‘the present King of 
France”’ determines the null class. Further, there is a universal 
class of which everything, excepting this class itself, is a mem- 
ber.? Every postulate and theorem of the system can be inter- 


1 See E. V. Huntington, Sets of Independent Postulates for the Algebra of 
Logic, cited above. 

2 This exception is necessary to avoid the difficulties involved in the notion 
of “the class of all classes.” See Whitehead and Russell, Principia Mathe- 
matica, ch. 2. Though the universal class is not a member of itself, still it is 
coextensive with itself; 7.e., the relation of class inclusion or subsumption, 
represented by the J-groups of the system, holds for it; so that (w(Zu)) is true. 


244. SYMBOLISM AND TRUTH 


preted as a true statement about classes, and every manipula- 
tion as a true inference, leading from premises to conclusions 
that concern classes, 

The original terms of the system, a, b, and ¢ stand for any 
classes; but since these terms are symbolically distinct, they can 
not, in any expression, be interpreted as signifying the same 
class. (Rab) means the class that includes all the members of a 
and 6, and only these members; this is called the “logical sum” 
of a and b. (Sab) means the class whose members belong both to 
a and 0; it is the “logical product” of a and b. (Na) means the 
class of all objects excluded by the class a. The symbol z stands 
for the null class, and wu for the universal class, for “nothing” 
and “everything,” respectively. The expression (b(Ia)) means 
that the class a is included in the class b. 

The rules of substitution tell us: 

(1) That any of the original terms can be mutually substi- 
tuted for one another, and that any of the basic groups, or 
groups derived from them, can be substituted for any of the 
original terms. Now if, on the class interpretation, (Rab), (Sab), 
(Na) and their derivatives represent anything, they will stand 
for classes. The logical sums, products, and negatives of classes, 
together with their derivatives, are themselves classes. Hence 
they can replace the variables a, b, and c in any expression and 
the expression will still be true, for a, b, and ¢ are any classes. 
Moreover, every sum and product might be the sum or product 
of a class and itself; so that every expression containing distinct 
symbols can be altered, by substitutions, into one containing 
tautologous symbols without rendering the expression untrue. 
(For the reason that groups formed by R, S, and N stand for the 
same general sort of entities, that is, classes, as those meant by 
their terms, these symbols of unity represent operations, rather 
than relations.) } 


1 See below, sec. vii. 








FORMAL DEDUCTION 245 


(2) The group (b(Za)), which means that the class a is in- 
cluded in the class 6, cannot, on the other hand, be substituted 
for a, b, and ¢, since it does not stand for a class. If a is included 
in b, the classes a and b are related, but this relation constitutes 
a new sort of fact, which is not itself a class. 

(3) The classes z and u can replace any of the original terms, 
a, b, and c, but these terms cannot replace z and u; for the null 
and universal classes are special elements, they are unique. 
What is true of any class is true of them, since they are classes, 
but the converse does not hold. 

(4) Equivalent groups or symbols can replace one another, 
for they represent the same class. Thus the null class is defined 
by and can be substituted for Sa(Na); it is the logical product 
of any class and its negative, that is, it is the class that includes 
all the members both belonging to and excluded by any class 
a— and these are no members. 

Obviously, these rules of manipulation make it possible, 
through the substitution of interpreted symbols or groups in 
other interpreted groups, to derive true propositions about 
classes from other true propositions about classes; they yield 
true inferences. 

The interpretations of the postulates are not so simple as 
those of some of the theorems. Theorem 1, Raz = a, is the fa- 
miliar proposition that “‘the logical sum of any class and the 
null class is identical with the first class,” that is, ‘the class in- 
cluding all members of a and of the null class is the same as a.”’ 
Theorem 2, Sau = a, states that “the class of members common 
to a and the class of everything is the same as a.” Definition E, 
z = Sa(Na), is the principle of contradiction for classes, and 
asserts that “‘a class and its negative have nothing in common.” 
Definition F, u = Ra(Na), is, on the other hand, the law of the 
excluded middle for classes; it affirms that “the class including 
all members of a and all members excluded by a is the class of 


246 SYMBOLISM AND TRUTH 


everything,” or simply “that a class and its negative exhaust the 
universe.’ Theorems 3 and 4, Raa =a and Saa = a, are two 
forms of the principle of identity for classes. The first states that 
“the class including all the members of a and of a is the class a”’; 
and the second, that “‘the class of members common to a and a 
is the class a.’’ Theorem 5, a = N(Na), that is, ‘‘the class that 
excludes all that is excluded by any class a is the class a,” is the 
principle of double negation; “‘not-not-a is identical with a.” 
Theorems 6 and7,z = Nuandu = Nz, show that the universal 
and null classes exclude, or are the negatives of, one another, 
that is, “nothing” excludes “everything” and “everything” 
excludes “nothing.” ! Theorem 8, Rau = u, states that ‘the uni- 
versal class added to any class a gives the universal class”; and 
this theorem differentiates the wu (and the “‘addition’’) of the 
class algebra from the number 1 (and the “‘addition”’) of ordi- 
nary algebra; 1 added to any number does not give 1. Theo- 
rem 9, Saz = z, however, shows an analogy between the null 
class and the zero of numerical algebra: “the logical product of 
any class a and the null class is the null class.”” Theorems 10 and 
11 are two forms of the principle of “absorption”: Ra(Sab) = a 
asserts that “any class a absorbs by addition a logical product 
of itself”’; and Sa(Rab) = a, that “‘any class a absorbs the sum 
of itself and another class in a logical product of itself and this 
sum.”’ Theorems 12 and 13 are forms of the principle of “‘trans- 
position”: Rab = N(S(Na)(Nb)) allows a sum of classes to be 
transposed into the negative of the product of the negatives 
of these classes; while Sab = N(R(Na)(Nb)) allows a logical 
product of classes to be transposed into the negative of the sum 
of the negatives of these classes. Theorems 14 and 15 are the “‘as- 
sociative”’ law for class sums and products, respectively. Postu- 
lates C and D are the “distributive” law; Ra(Sbc) = S(Rab) 


1 By theorem 18, “nothing”’ is also subsumed under or included by “every- 
thing.” The null class has the peculiar property of implying its own negative. 








FORMAL DEDUCTION 247 


(Rac) states that “the sum of aclass and a product of classes 
is the same as a product of two sums” (loosely put); while 
Sa(Rbe) = R(Sab) (Sac) states that “the product of a class and 
a sum of classes is the same as a sum of products” (loosely put). 
The symbols express this proposition more clearly than a brief 
form of words can, as is also the case with postulates A and B: 
Ra(Sb(Nb)) = a asserts that “if the logical product of a class 
and its negative is added to another class, the whole will be 
identical with this latter class”; and Sa(Rb(Nb)) = a asserts 
that “if the logical sum of any class and its negative forms a 
product with another class, the whole will be identical with this 
latter class.” 

The “commutative” law, Rab = Rba and Sab = Sba, does 
not appear in this system. It is unnecessary to state that “the 
logical sum or product of a and b is the same as the logical sum 
or product of 6 and a” for the reason that the spatial order of 
the symbols in the groups is not relevant to their significance. 
Rab is the same symbol as Rba, and Sab is the same symbol as 
Sba; the operations of class addition and class multiplication are 
symmetrical, and these symbolic groups — which are without 
order — represent them as such. 

The group (b(Ia)), however, has an order; “the class a is sub- 
sumed under the class b” means something different from “the 
class 6 is subsumed under the class a.’’ The order (6(Ta)) stands 
for the first of these facts, and the order (a(Ib)), for the second; 
and these differences of order are represented by the distribu- 
tion of the terms a and 6 in the two constituent groups of the ex- 
pression (a(Jb)), not by the spatial arrangement of the symbols. 

The theorems in terms of J-groups, interpreted as class inclu- 
sions or subsumptions, state the following propositions: Theo- 
rem 16, (a(Jz)), affirms that “the null class is included in any 
class,” that is, any class covers as great a logical area as a class of 
no members, and, if it is not itself a class of no members, covers 


248 SYMBOLISM AND TRUTH 


a wider area. Theorem 17, (u(Ia)), expresses the fact that “any 
class is included in the class of everything,” which is plainly true. 
Theorem 18, (w(Zz)), is, like theorem 16, paradoxical; it asserts 
that “the null class is included in the class of everything,” that 
is, that the universal class covers everything which is covered by 
the null class—and much more. Theorem 19, (a(I(Sab))), states 
that “any class includes the members common to itself and an- 
other class’’; and theorem 20, ((Rab) (Ia)), that “any class is 
included in the class formed by itself and another added to- 
gether.” Theorem 21, (a(Ja)), tells us that “‘any class includes 
and is included by itself.”” The definitions of class inclusion, G 
and H, are clearly true: (b(Ja)) = (Rab = b) says that “if a 
class 6 is identical with the class composed of all the members of 
a and 6, this is equivalent to the statement that } includes a’’; 
and definition H, (b([a)) = (Sab = a), says that “if a class a is 
identical with the class whose members are common to a and b, 
this is equivalent to the statement that a is included in 6.” 

All of the original postulates, definitions, rules of substitution, 
and many of the theorems of this deductive system are thus 
seen by inspection to be true for classes. But in order to verify 
the system as a whole for this interpretation, it is necessary to 
verify only the postulates, definitions, and rules of substitution, 
for if these original propositions hold for classes, all the propo- 
sitions derived from them will hold for classes. The reason for 
this will be apparent from a further consideration of the mean- 
ing of rules of substitution in general, and of the inferences to 
which they lead when they are interpreted. 


VI 


Symbolic groups built up from other symbolic groups or from 
simple terms are functions of these groups or terms. (We have 
observed before that the idea of a group is the same as that of a 
function.) Every symbol in an uninterpreted deductive system 





FORMAL DEDUCTION 249 


has a functional range, which is simply all the groups into which 
it can enter as a constituent. A rule of substitution lays down 
conditions determining the functional ranges of symbols; it tells 
us either that the functional ranges of two symbols coincide or 
that the one is wider than the other, that is to say, it prescribes 
what their functional ranges shall be. If it were possible to 
spread out on a single page all the groups of a symbolic system, 
there would be no need for rules of substitution; we could see at 
a glance what was the functional range of every symbol. But 
in all except trivial systems the number of possible groups is 
very great, usually infinite, and so rules of substitution are 
necessary. 

If a symbol z can be substituted for a symbol y in an uninter- 
preted system, the functional range of z is wider than that of Y 
that is, for every group in the system containing y as a member 
there is a group (similar in every other respect, both in its con- 
stituents and in its form) containing x as a member, but not the 
reverse. And if x and y can be mutually substituted for one an- 
other, their functional ranges coincide, that is, there are no 
groups in the system containing x which are not paralleled by 
groups (similar in every respect except for the presence of 2) 
containing y, and vice versa. 

This conception of the functional range of a symbol intro- 
duces a new kind of variability, functional variability, which is 
wholly different from the interpretational variability — inde- 
terminateness of reference — hitherto considered. A functional 
variable is a variable with respect to the groups in which it can 
play a part; and objects, no less than symbols, exhibit this type 
of variability. Just as a symbol composed of other symbols is a 
symbolic function, so an object composed of other objects, that 
is, a factual complex, is an objective function. We describe ob- 
jects through their predicates and relations; any object may 
have many different predicates and relations, it may enter into 


250 SYMBOLISM AND TRUTH 


many different complexes; and its functional range is all the 
complexes in which it can be a member. With respect to these 
groups the object is a variable; it may appear now in one group 
and now in another, and other objects may take its place in 
groups. Thus a deductive system, when it is interpreted, will 
describe a certain set of objects through certain selected func- 
tions of these objects. ¢ 

Strangely enough, the variables of wider functional range are 
the values of the variables of narrower range; the former are the 
more specific in meaning, while the ones of narrower range are 
the less specific. Thus, in the system now under consideration, 
the terms z and wu enter in functions in which the terms a, b, and 
c cannot play a similar part; z and wu are functional variables of 
wider range than a, b, and c, and hence are special values of the 
latter. (Theorem 6,2 = (Nu), for example, cannot be translated 
into z = (Na) ora = (Nu).) But the reason for this is evident. 
The more we know about an object, the more determinate it be- 
comes for thought, and the more functions in which a symbol 
enters, the more completely is its réle in the system fixed. 

A rule of substitution, then, lays down the conditions of func- 
tional variability for the interpretational variables of a symbolic 
system. In doing so it prescribes the form of the system and at 
the same time, through prescribing the form, imposes limitations 
on the interpretation. When the symbols are given (interpreta- 
tional) values, these values must be such that the facts into 
which they enter are of the same structure as the symbolic 
groups into which the uninterpreted symbols enter; and even so, 
a wide range of possible (interpretational) values is permitted to 
any of the symbols of the system. But the interpretation must 
always fulfill the conditions imposed by the rules of substitu- 
tion, and this requires that the objects meant by any symbol or 
group must have a functional range in the world of fact which 
corresponds to the functional range of this symbol or group in 








FORMAL DEDUCTION 251 


the uninterpreted system. This being the case, the manipula- 
tions of the symbols will always yield true propositions. 

Thus, if the terms a, b, and c, in the Boolean Algebra stand for 
classes and the symbols of unity R, S, and N signify the opera- 
tions of class addition, multiplication, and negation, it will be 
possible to substitute a, b, and c for one another for the reason 
that any class forms a sum or product with any other class, and 
also has a negative. The groups (Rab), (Sab), (Na), and their 
derivatives can be substituted for these terms, for these groups 
also signify classes (complex classes) and so can have sums, 
products, and negatives of their own. Every complex class en- 
ters into the same sort of class operations as every simple class. 
But the simple terms a, 6, and ¢ cannot replace the symbols 
for these complex classes for the reason that there are certain 
functions of complex classes which are not functions of simple 
classes. 

In the interpreted system, the rules of substitution cover a 
multitude of existential or “‘material”’ implications which hold 
for the objects meant. The rule which permits the substitution 
of (Rab), (Sab), (Na), for the terms a, b, and c informs us that 
“if there are classes, there are sums, products, and negatives of 
these classes’’; the provision that a, 6, and ¢ can be mutually 
substituted for one another tells us that “‘if there are functions 
of one class, there are similar functions of other classes.’ But 
these existential implications must not be confused with spe- 
cially postulated, and uninterpreted, implications of the sort 
mentioned before, which permit the substitution of certain sym- 
bols for others as conclusions in chains of deduction. When the 
system is interpreted, these specially postulated connections of 
meaning will be “formal” rather than existential implications. 
Thus, though (Na) yields by substitution (and hence existen- 
tially implies) the complex (N(Na)), this could not mean that 
(Na) “formally” implies (N(Na)), for this would assert that 


252 SYMBOLISM AND TRUTH 


“any negative implies its own negative.” The substitution really 
means that “the negative of a negative is an instance of a nega- 
tive,” or “if there is a negative of a class, there is also a negative 
of this negative.” } 

A symbol whose range of functional variability includes but 
does not coincide with that of another is a constant with respect 
to this variable of narrower functional range. The symbols z and 
u in the Boolean Algebra are constants with respect to the terms 
a, 6, and ¢, since z and u can be substituted for these terms, but 
not the reverse. Yet z and u are not completely determined in 
significance by this fact; there are still as many possible inter- 
pretations for them as there are for the system. A symbol whose 
meaning is variable in interpretation may function as a con- 
stant, when its part in an uninterpreted system alone is consid- 
ered. Such a symbol is a “functional constant,” and is known in 
mathematics as a parameter. Moreover, all the groups of our 
system are, with respect to the terms a, b, and c, functional con- 
stants; any one of these groups stands for some particular sort 
of combination of classes. Indeed, if the system is taken merely 
as an uninterpreted set of symbols, the only elements in it that 
function as variables are the terms a, b, and c. Every other ele- 
ment or expression is a value of these variables. Therefore, a, b, 
and c, which have the narrowest range of functionality in the 
system, are the “functional variables’’; and each of the substi- 
tutions of a group or other element (unless it be of the elements 

1 The notion that a rule of substitution is to be interpreted as stating a 
relation between the functional ranges of two variables makes it clear why 
symbols of indistinct meaning, 7.e., the symbols on either side of the sign of 
identity, can be mutually substituted for one another. When the system is 
interpreted, these symbols must always be given an identical value, they must 
stand for the same object; and obviously every object has the same functional 
range as itself. Further, it is clear that a coincidence of functional ranges, and 


hence a possibility of mutual substitution, is not the same as identity of 
meaning. 








FORMAL DEDUCTION 253 


a, b, or c) for a, b, and ce, puts a functional constant in place of 
one of these functional variables. 


VII 


The symbols of unity R, S, and N stand for operations. That 
they must stand for operations, and not relations, is determined 
by the deductive use made of the groups in which they appear. 
The distinguishing feature of an operational group is that it can 
be substituted in ctself for one of its terms; and in the Boolean 
Algebra this is provided for by the rule that (Rab), (Sab), and 
(Na) can take the place of a in any group, and hence in these 
very groups. In other words, an operational group is a value of 
the functional variables that enter into it. 

The “‘plus,” ‘‘minus,”’ and “‘times”’ of numerical algebra, for 
instance, are operations because the complexes they form are 
numbers. If a and b represent numbers, (a — b) will be a num- 
ber; it may be the number a, where b is zero, or the number 
(—b), where a is zero. But it will always be some number, and 
thus it can take the place of a or b in any algebraic expression 
and still give a number; it can be substituted in the very combi- 
nation (a — b), giving ((a — b) — b), which is a number. 

A relational group, on the other hand, is not a value of the 
variable terms that appear in it. If a and b are points, and (Rab) 
means “‘a follows b,”’ this fact is not also a point, and it cannot 
take the place of a or b in any complex of points. For this reason, 
the I of the Boolean Algebra is a relation rather than an opera- 
tion. The I-groupscannot be substituted for the terms that enter 

1 It is possible to consider these ‘‘constants” as functional variables of dif- 
ferent orders. What is a functional constant with respect to one symbol might 
be a functional variable with respect to another. The order of variability of the 
symbols is shown by the rules of substitution. Thus, in the Boolean Algebra 
(Rab) is a functional constant with respect to a and a functional variable with 
respect to (R(Rab)b), which is a special case of it. But for purposes of simplifi- 


cation, all the groups can be lumped together as constants with respect to the 
terms a, b, and c. 


254 SYMBOLISM AND TRUTH 


into them, for if a class a is included in a class b, this does not 


form a class, as does the logical sum or product or negative of a 
and b. 


Operations give rise to systems of an infinite number of possi- 
ble forms; an operational group can replace again and again a 
term which appears in this group itself, yielding each time a 
group of higher type. For every complex that contains a, in the 
Boolean Algebra, there is one of higher type that contains (Rab), 
(Sab), or (Na); so that a “proper part” of the collection of 
groups in which a is a member can be put into one-to-one corre- 
spondence with the whole of this collection. And this proves 
that these groups are infinite in number. 


1 For a definition of an infinite collection, see E. V. Huntington, The Con- 
tinuum, pp. 7 ff. 

? A set of postulates for serial order of the simplest sort illustrates the dif- 
ference between operations and relations, and also shows how a system wholly 
different from the Boolean Algebra is constructed: 

(1) Assume that a, 6, and ¢ are distinct symbols for terms; and that the 
system is built on the basic group (a(0b)) v (b(Oa)). (The symbols (v) and (.), 
which stand respectively for the logical ideas “or” and “and,” are used in the 
statement of the plan of this system; and if the system is to be completely un- 
interpreted, these symbols might be replaced by symbols that do not suggest 
these logical ideas, e.g., by L and N.) It will be observed that the grouping of 
the complex (a(0b)) shows that it has an order, irrespective of the spatial ar- 
rangement of the symbols; and that (b(Qa)) is the alternative order of this 
asymmetrical form. 

(2) The symbols a, b, and ¢ can be mutually substituted for one another; 
but distinct symbols must always be replaced by distinct symbols. 

(3) The special “formal” implication, (a(0b)). (b(Oc)) ““implies”’ (a(Oc)), 
holds in the system. 

It is apparent that (a(Oa)) or any combination in which this group might 
appear is not in the system; for the provision that distinct symbols must al- 
ways be substituted for distinct symbols will not permit us to derive (a(Oa)) 
from (a(0b)) or from any of the other O-groups. These O-groups are therefore 
wreflexwe. Further, the group (a(0b)) is, by its grouping, distinct from (b(0a)); 
and this is a distinction of sense, 7.e., of the distribution of the terms in the 
constituent groups. The O-groups are therefore asymmetrical for distinct 
terms. (Obviously, if there were an O-group of indistinct terms, e.g., (a(Oa)), 
this would be symmetrical; but there is no such group.) The implication 
(a(Ob)) . (b(Oc)) “implies” (a(Oc)), shows that the O-groups are transitive; 
but transitive only when a, b, and ¢ are distinct, for (a(Qa)). (a(Oa)) “‘implies” 
(a(Oa)), and (a(0b)) . (b(Oa)) “implies” (a(Oa)) cannot be derived from this 
implication without violating the rules of substitution. The fact that the O- 
groups cannot be substituted for the terms a, b, and ¢ shows that they are 





FORMAL DEDUCTION 255 


Vill 


The apparently arbitrary manipulations of the symbols of an 
uninterpreted system are “deductions” for this reason: that, 
when the system is interpreted, that is, when the postulates are 
asserted for a set of objects, these manipulations become infer- 
ences. The theorems are then asserted on the strength of their 
connection with the postulates; the truth of the postulates 
strictly proves the truth of the theorems. 

Inference is allied to assertion and belief. There is no such 
thing as a hypothetical inference, just as there is no such thing 
as a hypothetical belief. If a proposition is believed, it is re- 
moved from the realm of the hypothetical; it is no longer an idea 
merely entertained, but is accepted as true or, it may be, “‘ac- 


relational, rather than operational, groups; and since (a(Ob)) v (b(Oa)) is sig- 
nificant in the system, the terms a and 6 (or a and ce, and b and ¢, if these are 
properly substituted in this expression) are connected in one sense or the other 
by the relation O. This is the postulate of “connexity.” 

Now, a relation which is connected, irreflexive, transitive for distinct terms, 
and asymmetrical for distinct terms, is a “serial relation.” (See E. V. Hunting- 
ton, op. cit., pp. 11 ff.) If a, b, and ¢ stand for points on a line, and (a(0b)) 
means that “the point a precedes the point b, in the order left to right,” the 
postulates can be interpreted as follows: 

(1) Asserts that “any point precedes any other point, or this latter precedes 
it.” The condition that the points must be distinct is added by the second 
half of the rule of substitution under (2). 

(2) The first half of this rule of substitution asserts that “if there is a point, 
there are also two other points”; and the second half asserts that “if any 
point precedes a point, these two are distinct,” since only symbols that refer 
to distinct points can appear in the complex “a precedes b.”’ 

(3) Asserts that “if any point precedes a second, and this second precedes a 
third, the first point precedes the third.” 

That the proposition (a(0b)) . (b(Oa)), t.e., “a point a precedes point b and 
this latter point also precedes a,” does not hold in the system is proved by the 
fact that in order to derive this group from the similar group in the implica- 
tion, (a(0b)). (b(Oc)) “implies” (a(Oc)), we must assume a contradiction; we 
must suppose that a is a distinct symbol from a. With this supposition, a can 
be substituted, according to the latter half of rule (2), for c in this implication, 
giving (a(O0b)) . (b(Oa)) “implies” (a(Oa)). But if a ¥ a, this is a violation of 
the principle of contradiction, which is always assumed as a general rule of 
symbolism. 


256 SYMBOLISM AND TRUTH 


cepted as false,’’ which means that its negative is accepted as 
true. And similarly, a proposition that is inferred from another 
is accepted as true (or false), not because it is verified in itself, 
but because it is believed to be connected in a certain way with a 
proposition previously accepted as true (or false). Inference is 
the passage from a belief, by way of a belief, to a belief, and is 
expressed by the assertion of a premise and of a connection be- 
tween this premise and a conclusion, followed by the assertion of 
the conclusion. The connections on which inferences rest are im- 
plications. (There arc, however, certain types of inference — 
probable or inductive inferences — which do not rest on the 
strict implications considered here.) 

It is characteristic of true propositions that they can stand 
alone as objects of belief. Though most propositions have their 
“reasons,” that is, their premises, by which they are implied, 
any truth can be severed from its premises and believed on its 
own account. Its truth does not consist merely in the “reasons” 
that can be given for it. If it is true, it is equally true apart from 
the propositions which imply it, equally true with or without 
“reasons.”’ If it were necessary to remember all the logical con- 
nections of a proposition believed, belief and assertion would be 
difficult undertakings; but fortunately the premises of a belief 
can be forgotten without destroying the truth of the proposition 
believed (if it is true). Therefore inference, since it leads from 
one proposition believed to be true to another believed to be 
true, is well described as “the dropping of a true premise . . . the 
dissolution of an implication.” ! 

But a premise which is not believed cannot be dropped, and 
for this reason the asscrtion of a chain of implications is not an 
inference. “‘p implies q” means that whenever p is true, q is true; 
but it does not assert the truth or falsity of p or of q; it merely 
excludes the possibility that “‘p is true and q false.” So far as its 


1 Whitehead and Russell, Principia Mathematica, p. 9. 





FORMAL DEDUCTION 257 


constituent propositions are concerned, a true implication is still 
hypothetical; though a connection between p and q is asserted, 
p and q themselves are still entertained and not believed. And if 
the supposition that the premise of this implication is true is 
added, this supposition will not result in an inference to the 
truth of q; it will yield nothing but the supposition that q is true 
“if p is true and p implies g.” One might go on forever asserting 
implications and supposing that their premises are true without 
performing an inference. The chain of implications is broken 
only when the premises, as well as the implications themselves, 
are asserted. Every one of the series of propositions which are 
believed to be connected by these implications can then be be- 
lieved, by themselves, to be true. 

Inference is, in short, a form of judgment and, like all judg- 
ment, it takes the leap of belief; it introduces a new attitude of 
mind toward propositions. But it differs from simple judgment 
in that it must take two leaps of belief; it must accept the truth 
of an implication (or series of implications) and of the premise of 
this implication (or series of implications). Thus, from survey- 
ing propositions and asserting that they are connected in certain 
ways, it passes to the affirmation of these propositions apart 
from their connections. 

That a belief in the truth of a proposition implied by a true 
premise is justified follows from the nature of implication. Any- 
thing implied by a true premise is true; for the truth of the im- 
plication, “‘p implies g,”’ does not admit the possibility of p be- 
ing true and q false. To believe p, and to believe that Pp implies 
certain propositions, is inconsistent with believing that these 
latter propositions are false. And though one is not compelled to 
believe the consequences of p when he believes p (for he always 
has the alternative of being sceptical), he cannot consistently 
believe that these consequences are false. Here as always the 
goal of his belief is consistency. 


258 SYMBOLISM AND TRUTH 


The two principles which underlie inference, then, are: (1) 
that any true proposition is true apart from its connections with 
other propositions, and can be asserted on its own account; and 
(2) that a true implication and a true premise always yield a 
true conclusion. These principles permit us to move in thought 
from one assertion or belief to another; to wipe the slate clean 
and start afresh with each new conclusion. 

When a formal deductive system is taken to refer to certain 
objects, it is asserted, and if its postulates and rules of substitu- 
tion are true for these objects, the conditions necessary for in- 
ference are satisfied. But it is more important still to observe an- 
other fact which follows from the complete interpretation of a 
deductive system. The conditions of truth and of significance in 
the system become the same. Every proposition which has a mean- 
ing is true, the system contains no significant propositions which 
are false. 

The symbolic manipulations, which are the inferences of the 
asserted system, arise in the unasserted (purely hypothetical) 
system from rules of syntax which prescribe how the symbols 
are to be taken together as significant groups — rules analogous 
to rules of grammar. General principles of symbolism, a “uni- 
versal grammar,” necessary in all systems or “languages,” are 
laid down, and within this framework special conditions of sig- 
nificance are provided for, so that each deductive system be- 
comes a special “language.” Its postulates state nothing more 
than what expressions are to be considered significant, what 
symbols are identical in meaning, and what symbols can be sub- 
stituted for one another without rendering the expressions in 
which they appear meaningless. The system differs from more 
concrete languages in that its “words” and “phrases” refer to 
no objects but are variables, grouped about certain fixed ele- 
ments, v2z., certain logical forms. These logical forms are the 
sole subject-matter of the uninterpreted language; they are em- 








FORMAL DEDUCTION 259 


bodied in the “words” and “phrases,” the symbols and groups 
of symbols, but they are not asserted to exist elsewhere. The 
language asserts no truths but simply surveys logical forms. On 
the other hand, when the system is completely interpreted, the 
language that previously asserted no truths becomes a language 
that asserts nothing but truths; there is no expression in it which 
is both significant and false. 

The so-called “false propositions” of a completely inter- 
preted deductive system are “pseudo-propositions,”’ that is, 
meaningless collections of the symbols, and not significant 
groups permitted by the syntactical rules. Such “ pseudo-propo- 
sitions” can be introduced only by violating the conditions of 
significance. In the postulates for serial order,! for example, the 
group (a(Oa)) does not enter; it is nonsense so far as the syntac- 
tical plan of this “language” is concerned. Interpreted as the 
system is interpreted, this pseudo-proposition asserts that “any 
point, a, precedes itself,” but though this idea can be expressed 
in words, it cannot be significantly stated in the symbols of the 
system. T’hus it is superfluous (in fact absurd) to say that 
(a(Oa)) is false, for only a significant expression can be false. 

Completely interpreted deductive systems are therefore com- 
pletely inferential. Every transformation which conforms to the 
“grammar” of the system is an inference; every “grammatical” 
expression is true. 


IX 


Ordinary language, on the contrary (as well as the system of 
mental images), is incompletely inferential. The conditions of sig- 
nificance and truth for its expressions are not the same. Clearly 
if one follows merely its grammatical rules, he will not be led 
from true premises to true conclusions. Only some of the manip- 
ulations of its words and phrases will be inferences. But the pro- 
cess of thought, as it is carried on in language and in images, 


1 See above, sec. vii, note. 


260 SYMBOLISM AND TRUTH 


presents an interesting analogy to the transformations of formal 
deductive systems, for thought in these former media is also the 
manipulation of symbols. 

Thought has two aspects: it is both dynamic and static; 
and inference belongs to its dynamic side. Inference is a 
movement of thought coupled with belief, but strict inference 
arises in a wider setting of thought-movement — a setting 
which Hobbes calls “mental discourse” or the “train of imagi- 
nations.” 

“Mental discourse,” beginning with presented objects, mir- 
rors a world of fact in a world of representations; it builds simple 
symbols which refer to objects into complexes, which may or 
may not correspond to objects. The drama of “‘ideas”” makes use 
of symbols as its puppets; the symbols combine and recombine, 
the puppets move on the stage, and one grouping succeeds an- 
other to the end of the piece. Words and images are the primary 
instruments of this “mental discourse.”” They combine, dissolve, 
and recombine, pass and repass in new and changing unities, 
and here and there they precipitate a reference to fact. Such 
discourse is the free play of the imagination, musing or dream- 
ing, rather than deductive reasoning, but it is akin to deduc- 
tive reasoning in that it is a process of substitution within a 
plan of syntax. Images (both simple and complex), words, and 
phrases, take the places of one another in groups; the group that 
was now of one form assumes a different form; but throughout 
all these mutations, the plan of syntax on which the system of 
images or of words is based is never violated. The “mental dis- 
course”’ confines itself within the limits of intelligibility which 
this plan imposes. Yet this discourse is not inference, as it would 
be in a completely interpreted deductive system, for the plan of 
syntax within which it is carried forward cannot be so inter- 
preted that every significant proposition to which it gives rise is 
true. There is no difficulty in abandoning fact for fancy within 





FORMAL DEDUCTION 261 


the systems of language and images; but ina completely inferen- 
tial system nothing that is conceivable is false. 

We cease to dream and begin to infer when our purpose in the 
manipulation of symbols is to arrive at truth. A completely in- 
ferential (and interpreted) deductive system is so constructed 
. that this purpose can be accomplished merely by following its 
tules of significance, for these rules sum up a multitude of impli- 
cations which hold for the subject-matter. But the syntactical 
plans of language and the imagination do not run parallel to 
logical connections of the subject-matter. In these media, only 
a limited number of expressions will imply or be implied by 
others, and so can be inferred from others. These expressions 
will form a solid island of true inferences in a sea of fancies. Yet 
there is a marked analogy between free imagination, “mental 
discourse,” and formal deductive inference. The constructive 
imagination is a genus of which the process of formal deduction 
is a species; imagination is necessary to reason. 


Xx 


The principal points that have been brought forward in this 
examination of formal deduction are the following: 

For formal logic, all that is essential in any subject-matter is 
its logical structure, and this structure can be isolated and stud- 
ied in itself through uninterpreted symbols whose forms and 
their connections alone are considered. Such uninterpreted sys- 
tems of symbols are not without meaning, however. In the con- 
text of logical structure, all the elements of these systems, with 
the exception of their logical forms, are variables, that is, sym- 
bols of undetermined meaning; and the groups as wholes have 
significance, though they refer to no objects, for any symbolic 
group with a structure is significant. The forms to be studied are 
presented in the very symbols through which they are studied. 

The postulates of these systems are plans of syntax which de- 


262 SYMBOLISM AND TRUTH 


termine what groupings of the symbols are permissible, that is, 
what the possibilities for thought in the system are; and the 
whole becomes a special “language” with a “grammar”’ of its 
own marking the boundary between sense and nonsense for the 
system. All special plans of syntax assume the general principles 
of symbolism: (1) the principle of group significance; (2) the dis- 
tinction between symbols of unity and terms; (3) the law of 
identity and (4) the law of contradiction. From these principles, 
it follows that the system must be composed of groups of terms 
joined by symbols of unity; the same symbols must always be 
used with the same significance, though symbols of different 
characters and forms can be taken as identical in meaning; and 
symbols that are originally distinct in meaning must always be 
distinct. 

All the significant complexes of the system are derived from 
certain basic complexes by substitutions, and this process of 
transformation by substitution 7s formal deduction; it is the 
manipulation of symbols within a plan of syntax. Two general 
rules of substitution are always followed: (1) the same symbol 
can be substituted for the same symbol, and symbols of identical 
meaning can be substituted for one another, in any complex; (2) 
all substitutions must be carried through completely. In addi- 
tion to these general rules, every system has its special rules of 
manipulation, and among these may appear certain “equations 
of structure,”’ definitions, and specially postulated implications. 
The latter permit the substitution of one group for another only 
when this other group appears as a conclusion of a series of de- 
ductions. Deduction in these systems is nothing but the manipu- 
lation of the symbols according to these rules, as is illustrated by 
the Boolean Algebra, which, though it can be completely inter- 
preted in terms of classes and class relations and operations, can 
be stated as a system of uninterpreted groups and rules of sub- 
stitution. 





FORMAL DEDUCTION 263 


A rule of substitution, in general, is based on a relation be- 
tween the functional ranges of the variables. If symbols coincide 
in their ranges of functional variability, they can be mutually 
substituted for one another; and if the range of one includes 
that of another, the former can be substituted for the latter, for 
it will be a functional value of the latter. With respect to vari- 
ables of a less inclusive range, those of wider range are “func- 
tional constants’’; while the variables of narrowest functional 
range in any system — those for which all other expressions of 
the system can be substituted, but which can not be substituted 
for these expressions — are the most general “functional vari- 
ables” of the system. Both functional constants and functional 
variables are undetermined in meaning; both are ““interpreta- 
tional”’ variables. 

If a group is a possible value of the variable terms which enter 
in this group itself, this group is operational rather than rela- 
tional. Operational are distinguished from relational complexes 
by the use which can be made of them in formal deduction, by 
the fact that they can be substituted in themselves for their own 
terms. Thus they give rise to an infinity of distinct possible 
forms. 

When a deductive system is interpreted, the arbitrary manip- 
ulations of the symbols become inferences, for the postulates 
and rules of substitution then embody implications, and if the 
postulates are true, the theorems are also true. To perform an 
inference is to pass from a premise that is believed, by way of an 
implication that is believed, to a conclusion that is believed on 
the strength of these other beliefs. Inference cannot be sepa- 
rated from belief and assertion; it cannot be purely hypothetical 
and the principles on which it rests are: (1) that any true propo- 
sition is true, and can be asserted, apart from its premises; and 
(2) that what is implied by a true proposition is true. Inference 
is “the dropping of a true premise.” 


264 SYMBOLISM AND TRUTH 


In a completely interpreted deductive system, whatever is 
significant is true; any of the permitted transformations of 
meaning lead from true premises to true conclusions, so that 
these systems are completely inferential. They are to be con- 
trasted with zncompletely inferential systems, such as language 
and the imagination, in which there is a discrepancy between 
significance or conceivability and truth. Though these latter 
systems resemble the former in that thought is carried forward 
in them by the manipulation of symbols within a plan of syn- 
tax, they differ from the former in that the pursuit of their rules 
of significance, alone, gives rise to fancy and free imagination 
rather than to inference. 

These formal deductive systems, in which everything but the 
logical structure of the matter referred to (if there is a matter 
referred to) is pruned away, show much more clearly than other 
symbolic systems how symbols copy the forms of facts and why 
the logical structure, which is present in the symbols as it is in 
the objects, is the essential bond of meaning between the mind 
and its objects. The mirror of thought, which reflects in the be- 
ginning a world of concrete facts, may send back a reflection of 
forms alone and these forms may belong to no world of fact, 
they may be merely possibilities for thought embodied in sym- 
bols. But the structure of these possible concepts will determine 
what they can stand for; if they represent objects, these objects 
must correspond to them in logical form. Whether formal de- 
ductive systems are interpreted or uninterpreted, thought 
reaches in them its maximum of clarity.! 


1 The views of formal deduction and truth here set forth are closely similar 
to those of Leibniz as interpreted by L. Couturat in La Logique de Leibniz 
(Paris, 1901). ‘“‘In an unpublished fragment relating to the universal lan- 
guage,” says Couturat (pp. 88, 89), “‘Leibniz imposes another condition on 
signs: it must be possible to deduce from their form alone, and from their 
composition, all the properties of the concepts which they represent. . . . Their 
combinations must depict for the imagination the logical connections of the 
corresponding concepts, so that the composition of the signs agrees with the 








FORMAL DEDUCTION 265 


composition of the ideas, following an exact analogy. . . . Moreover, not only 
does the symbolism translate the thought under an intuitive form, but it 
serves also to guide, to relieve, and even to supplant or replace thought. Just 
as the combinations of the ideas are represented by combinations of the corre- 
sponding signs, so the operations of the mind — that is to say, the reasoning 
which is carried on with these ideas — is expressed in concrete and sensible 
operations performed on the symbols. The abstract laws of logic are thus 
translated into intuitive laws which govern the manipulations of signs.” 

To the nominalism of Hobbes “Leibniz replies peremptorily,” continues 
Couturat (pp. 104, 105), “that, if signs are arbitrary, the relations between 
signs, which express or constitute propositions, are in no sense arbitrary; and 
that they (signs) are true or false according as they correspond or not with the 
relations of the things signified. Thus truth consists in the connection of signs 
so that they agree with a real and necessary connection of ideas or objects, 
which does not depend on us; or, in other words, it consists in that similarity 
of the relations of signs and the relations of things which constitutes an 
analogy in the proper mathematical sense of the term, that is to say, a propor- 
tion or equality of relationships. . . . The choice of signs and the definitions of 
words can, then, be arbitrary, but the linkage of the words and signs does not 
become so; and it is in this linkage alone that truth and falsity reside. We can 
even change the system of signs at will without changing a truth or making it 
dependent on our wishes; for, whatever symbols are chosen, there will be an 
arrangement of these symbols — and only one arrangement — which will be 
true, that is, which will correspond to the real order of things or facts. There is 
then an analogy, not only between signs and objects, but between different 
systems of signs in so far as they express the same reality. 

“This necessary rather than arbitrary order which exists in things is, 
though unknown, the objective basis of all truth. Once a certain system of 
arbitrary signs or a certain set of conventional definitions has been adopted, it 
no longer depends on us what combinations are true and what false; and this 
proves that truth, although it resides solely in our minds, rests on a principle 
outside us and expresses symbolically a reality of some sort.” 


CHAPTER VIII 
THE METAPHYSICS OF KNOWLEDGE 


I 


A tHEory of knowledge must come at last to metaphysics, for 
the aim of knowledge is to grasp reality, and without some no- 
tion of what reality in the broadest sense of the term is, we can- 
not say whether knowledge succeeds or fails. The limited reality 
of which we have spoken up to this point — which can be 
given in or inferred from an experience consistent with the 
whole of knowledge — is not enough. It is always possible that 
what can be thus given or inferred is merely an appearance, and 
that reality is something deeper, inscrutable to perception and 
perhaps even to reason. And so we must set out without any arti- 
ficial restriction of our concept of reality to answer, or rather to 
sketch the barest outlines of answers, to these fundamental 
questions: Can reality be known? If so, what is reality and how 
is it known? 

The first question is prompted by the sceptical impulse of 
knowledge to self-criticism; it arises from a mood of doubt which 
is unfamiliar to very few men. Walt Whitman speaks of this 
mood as “‘the terrible doubt of appearances, 


Of the uncertainty after all that we may be deluded; 
May-be the things I perceive — the animals, plants, men, hills, shin- 
ing and flowing waters, 
The skies of day and night — colors, densities, forms — 
May-be these are (as doubtless they are) only apparitions, and 
the real something has yet to be known.! 


1 Walt Whitman, “Of the Terrible Doubt of Appearances,” first published 
in Leaves of Grass, 1860. 





THE METAPHYSICS OF KNOWLEDGE 267 


Most of us easily shed this “terrible doubt of appearances.” 
Practical life obscures it, common sense engulfs it, and only 
poets, mystics, and metaphysicians are left to worry over it. 
But those whom it haunts find that there is no compromising 
with it; either all knowledge gives way before it or else thought 
is driven back and back till it touches first principles — and lays 
the foundations of a system of metaphysics. 

The peculiar thing about this question is that it cannot be sig- 
nificantly answered in the negative. Either we are condemned to 
perpetual asking without an answer or else we know reality. The 
sceptical impulse of knowledge to self-criticism defeats itself, at- 
tains no end, unless there is knowledge, not merely knowledge 
of appearances but of reality. A criticism of knowledge makes 
use of the very thing it criticizes, and unless the argument is to 
become circular or lead back indefinitely from premise to prem- 
ise, the knowledge on which the criticism is based must itself 
be exempt from criticism.! If knowledge fails (in some sense) to 
grasp reality, in knowing this fact it attains an ultimate truth 
and does not fail completely; and if it succeeds, the knowledge of 
why it succeeds cannot stand in need of justification, and so on 
through a series of justifications that has no end. 

This suggests either that no final criticism of knowledge is 
possible, that suspension of judgment is the way of sanity (and 
this means equally that knowledge cannot be vindicated or dis- 

1 This idea is clearly put by Aristotle; see W. D. Ross, Aristotle (1924), 
p. 45. “There are, says Aristotle, two errors (with respect to the ultimate 
validity of knowledge) which rest on a common basis. There is that of suppos- 
ing that knowledge implies either an infinite regress from premise to premise 
in order that nothing may be accepted as unproved, or else the acceptance of 
unproved and therefore unknown premises, and that knowledge is therefore 
impossible. And there is the error of supposing that knowledge is possible but 
proceeds in a circle — truth being thus reduced to the mutual implications of 
propositions none of which are independently known to be true. The common 
basis of the two errors is the assumption that proof is the only way of know- 


ledge, and against them both he affirms his principle that there are first prem- 
ises which neither need nor admit of proof.” 


268 SYMBOLISM AND TRUTH 


credited); or that there are first principles, final insights into the 
nature of the real, on which all knowledge rests. The former al- 
ternative is scepticism; the latter, the necessary starting-point 
of any metaphysics. 

And yet there have been attempts to compromise with doubt 
by answering this initial question — can reality be known? — in 
the negative, attempts to maintain that knowledge is of appear- 
ances only and that reality is hidden and unknowable. Herbert 
Spencer makes his bow in the opening chapters of his First Prin- 
cuples to the eternal mysteries of the universe, leaving this empty 
but venerated realm of the Unknowable to religion and meta- 
physics, and choosing for science the full and certain area of the 
Knowable. A strange, unstable dichotomy! There is to be no 
poaching of metaphysics and religion on science, and none of 
science on religion and metaphysics. Each goes its own way, 
metaphysics to the Unknowable, which is the real, and science 
to the Knowable, which is the unreal or half-real. Metaphysics 
becomes an unfulfilled aspiration toward the ultimate, and sci- 
ence a description of phenomena which, so far as we can tell, are 
less than shadows flitting before the senses. 

The agnostic compromise with doubt attains no better suc- 
cess than this. Clearly it is no compromise. Agnosticism is not a 
half-way house on the road between scepticism and meta- 
physics. There is no half-way house. If one accepts any truth, he 
accepts a standard by which he discriminates the true from the 
false, and beneath this standard is found his metaphysics. From 
the beginning of thought a concept of reality is present, making 
itself clearer as thought goes forward but never abandoned — 
unless thought thins out into scepticism. 

Men are for the most part neither self-conscious metaphysi- 
cians nor self-conscious sceptics; the temper of most minds 
strangely blends these two tendencies. But if either of these in- 
compatible strains is brought to light, it must exclude the other. 





THE METAPHYSICS OF KNOWLEDGE 269 


The scepticism which is fully aware of itself witholds all belief, 
ventures on no single affirmation, — not so much as the affirma- 
tion that belief is fruitless and unjustified, —and is thus reduced 
to silence, or at best to a vagrant roaming among possibilities, 
none of which is affirmed to be actual. But if one asks himself 
how it is that he can assert any truth, even the most meagre, he 
begins to uncover a metaphysics, for truth is never anything 
less than knowledge of the real. To become alive to any truth he 
must bring to the surface of thought the concept of reality he 
now discovers to be buried there. 

The description of knowledge which has occupied us so far 
takes its departure from the point of view of the plain man and 
hence is neither self-consciously sceptical nor self-consciously 
metaphysical. It appeals to experience in a wide meaning of the 
term, witholds judgment on ultimate questions, but at the same 
time is aware of its assumptions and does not assert that they 
are more than assumptions. The upshot of the positive theory 
of knowledge is this: the truth of ordinary experience is the cor- 
respondence of concepts through their structure with real ob- 
jects, and this reality can be given in or inferred from an experi- 
ence consistent with the whole of knowledge. Whether reality 
as such has a structure, whether the objects that appear in ex- 
perience are finally real, whether the mind in knowing is sepa- 
rated from or joined to an ultimate reality — all these ques- 
tions remain untouched. And yet, if they are swept aside, the 
door is left open for scepticism. In the face of these questions 
the limited truth and reality of the positive theory of knowledge 
must expand into a final truth and a full reality or contract 
into a flux of impressions and ideas — leaving only doubt. The 
positive theory of knowledge, including as it does the two 
incompatible strains, is unstable; it is a metaphysics tinc- 
tured with scepticism, a scepticism tinged with metaphysics. 
The task of speculative philosophy is to bring to complete self- 


270 SYMBOLISM AND TRUTH 


consciousness the one or the other of these warring attitudes 
of mind. 

It is this aim which distinguishes speculative philosophy from 
the special sciences. Science tolerates the frame of mind that 
joins scepticism to the assertion of truths. The scientist does not 
doubt that he is approaching a completer knowledge of reality, 
though he could not say why this is so without becoming a meta- 
physician; and yet he refuses all commerce with ultimates and 
thinks of his premises as working assumptions which he is not 
averse to discarding for better ones. Hesitating to affirm that he 
has reached a final truth, the scientist still believes that his 
growing knowledge is an indefinite approximation to such a 
truth. Here the metaphysician makes his point. If one’s stand- 
ards of truth are not themselves finally true, if one does not in 
some way already grasp reality when he sets forth on the jour- 
ney of thought, he cannot even conceive of attaining truth. 

The method of science is the method of assumption, hypothe- 
sis, postulation, and this way of thought falls between scepti- 
cism and metaphysics; it holds the two in an unsteady balance 
within itself. A full-grown metaphysics cannot rely on postu- 
lates or assumptions, for if these assumptions are false the whole 
of knowledge collapses, and assuming them to be true does not 
make them true. A full-grown scepticism, on the contrary, is 
equally receptive to all assumptions, not excluding contradic- 
tory ones. 


II 


A tradition of critical philosophy which purports to be neither 
sceptical nor metaphysical, nor yet to be poised as are the spe- 
cial sciences between these extremes, appears in the thought of 
the eighteenth and late seventeenth centuries. Kant is the 
father and Locke the forerunner of this more carefully reasoned 
agnosticism. By an examination of the nature of knowledge; 
this critical philosophy hopes to determine whether or not meta- 





THE METAPHYSICS OF KNOWLEDGE 271 


physics is possible, and it concludes that metaphysics is impossi- 
ble — that knowledge, being limited not only in extent but in its 
very essence, cannot penetrate through appearances to reality. 

The distinction between appearance and reality is as old as 
thought; indeed philosophy was bred in the suspicion that the 
real world is not what it appears to be, and the first philoso- 
phers set out with the confidence of adventure to discover the 
ultimate beneath the surfaces of things. But a second suspicion 
followed speedily on the first: that knowledge is without power 
to reach this ultimate. And so thought turned inward, its confi- 
dence shaken, to a criticism of its own capacities and aims. 

Whether knowledge is able impartially, and without begging 
the question by assuming its own validity, to criticize itself, is a 
query that does not occur to the agnostic. Pretending with Kant 
that this self-examination of thought will show whether a final 
truth can be reached, the agnostic forgets that his own theory is 
built on a metaphysical first principle, and that he himself 
claims one final insight — namely, that knowledge is confined to 
appearances. ‘Though all other truths are in his opinion limited 
and phenomenal, this truth — that we cannot know the ulti- 
mate — is absolute. 

Stated thus in outline, critical agnosticism appears self-con- 
tradictory. It is as if we were saying that by sight man can dis- 
cover that he cannot see. Yet both Locke’s Essay Concerning 
Human Understanding and Kant’s Critique of Pure Reason, hav- 
ing begun with the conviction that knowledge by internal criti- 
cism can reveal its own frailties, arrive at this conclusion. Kant 
and Locke have fostered a tradition which gives epistemology a 
peculiar authority in the field of philosophy, but their episte- 
mology is in reality a metaphysics. The philosophy that Kant 
terms critique is speculation of a most insidious sort, disguising 
itself as it does under another name. Though its aim is to dis- 
cover “whether such a thing as metaphysics be at all possible,” 


272 SYMBOLISM AND TRUTH 


it is itself impossible without the metaphysics whose wings it 
hopes to clip. The epistemological tradition of Locke and Kant 
is an unsuccessful attempt to straddle the issue between scepti- 
cism and metaphysics. 

Before the Kantian critical philosophy was born, a reply to 1t 
was framed by one of the metaphysicians whose dogmatism 
Kant condemned. In Spinoza’s Tractatus de Intellectus Emenda- 
tione, Kantianism is forestalled by the following argument: “In 
order to find the best method of investigating what is true, we 
must not stand in need of another method to investigate this 
method of investigating, nor in need of a third one to investigate 
the second, and so on to infinity. For by such a method we can 
never arrive at a knowledge of what is true, nor at any knowl- 
edge whatever. For it is the same thing as with artificial instru- 
ments, of which we might argue in the same manner. For inorder 
to work iron a hammer is needed, and in order to have a ham- 
mer it must be made, for which another hammer and other in- 
struments are needed, and so on to infinity; and in this manner 
any one might vainly endeavor to prove that men have no 
power of working iron. But in the same way as men in the be- 
ginning were able with great labor and imperfection to make the 
most simple things from instruments already supplied by nature 

. so also the understanding by its native strength (vis sua 
nativa) makes for itself its intellectual instruments wherewith it 
acquires new strength for other intellectual works, and so gradu- 
ally proceeds until it attains the summit of wisdom.” ! This na- 
tive strength of the intellect is its power of insight into reality, 
which is present in thought from the first. 

The severance of appearance from reality, on which most 
criticisms of knowledge are based, may be more or less com- 
plete. It may be sharp and irreparable as in Kant, or it may be 
partial and reconcilable as in the Absolute Idealists, who be- 


1 B. de Spinoza, T'ractatus de Intellectus Emendatione, sec. 6. 





: 
. 
| 


THE METAPHYSICS OF KNOWLEDGE 273 


lieve that “there is no truth but the whole truth,” and yet that 
no appearance is denied its small grain of reality and truth. The 
breach between appearance and reality once opened must be 
healed, and the reason is not far to seek. What appears must 
have some sort of reality or it could not appear; it would be 
simply nothing. The important question then is, not how are 
appearance and reality separated, but how are they united? — 
how, in Spinoza’s language, does reality manifest itself in attri- 
butes and modes? To hold that there is a world of absolute ap- 
pearance cut off from a world of absolute reality, as Plato’s 
realm of opinion is from his realm of ideas! and Kant’s nou- 
menal realm from the phenomenal, is to fall into a difficult di- 
lemma. Either the world of absolute appearance or the world of 
absolute reality should be dropped; the two refuse to stand side 
by side unrelated. Just as Aristotle attempted to bring the Pla- 
tonic ideas into the concrete matter of experience, so the Post- 
Kantians attempted to raise the Kantian phenomena toward 
the level of the noumena by making the phenomena finite parts 
of an infinite and absolute whole. 


iil 


Before we consider ways of healing the breach between ap- 
pearance and reality, let us examine the breach itself in its most 
extreme form, as it occurs in Locke and Kant. It arises here 
from a theory of mind-isolation which places appearances in the 
knowing subject and leaves reality out in the cold beyond the 
grasp of the knower. 

Locke’s metaphysics of mind-isolation rests on two premises: 
that “all our knowledge is conversant only with ideas,” and 
that ideas are of qualities only, never of substances, which are 
the substrata of qualities. Locke’s view presupposes the passiv- 


1 There is a question as to whether Plato intends completely to sever his 
two worlds. 


274 SYMBOLISM AND TRUTH 


ity rather than the activity of mind; a static screen of ideas im- 
poses itself from outside between the knower and reality, never 
to be swept aside. 

This is the crudest and simplest statement of the mind-isola- 
tion theory —the theory of epistemological dualism. Since 
Berkeley, it has had little currency in this form. The crux of 
Locke’s argument is the second premise, the distinction be- 
tween substance and its qualities; but just why substance, 
which Locke sometimes says is known in a confused way and 
other times not known at all, should be retained — why qual- 
ities (appearances) do not make up a self-sufficient and com- 
plete reality — does not become evident. Locke’s substance is 
nothing more than an arbitrary limit set to knowledge for no 
other reason than to satisfy the common-sense prejudice that 
things must have a substratum in which their qualities inhere, 
and the slender thread that holds together substance and its 
qualities snaps under the tension of Berkeley’s criticism; qual- 
ities alone are left, the unknowable xz, substance, being can- 
celled out. 

Locke’s first premise, that “knowledge is conversant only 
with ideas,” supports the theory of mind-isolation if one thinks 
of ideas as essentially disparate from real objects and (in Locke’s 
language) real qualities. One can for example suppose that real 
objects cause ideas different from themselves. How one can 
know this is another question, for apparently he must go be- 
yond ideas to do so. Therefore, if knowledge is conversant only 
with ideas, it is by hypothesis not conversant with objects which 
cause, bound, or limit ideas; and so the statement that knowl- 
edge is restricted to ideas has no foundation, unless it affirms 
merely that “we know what we know.” This is again the typical 
difficulty of agnosticism: if the mind is isolated, it would need to 
escape its isolation to know this fact. 

Though Kant’s formulation of the theory is more profound 


THE METAPHYSICS OF KNOWLEDGE Q75 


than Locke’s, it comes in the end to the same thing — agnosti- 
cism and mind-isolation. Kant does not argue from the distinc- 
tion of substance and its qualities, and he supports the notion 
that knowledge is conversant only with ideal objects by nega- 
tive if not by positive proofs. Kant insists as against Locke that 
the mind is active in cognition; this is perhaps his most impor- 
tant observation on knowledge as a whole. Yet from this prem- 
ise he draws the amazing conclusion that in the very act of 
knowing the mind shuts out from itself the reality (the thing- 
in-itself), and thus becomes ignorant of what it is striving finally 
to reach. As soon as the work of knowledge begins, the mind like 
a snail in its shell withdraws within itself. The concepts (cate- 
gories and forms of perception) which determine the mind’s 
essential directions of activity, far from causing it to expand 
outward to a fuller apprehension of the real, which it has some- 
how touched in “‘the original receptivity of the senses,” turn it 
away toward ideal objects which correspond in no intelligible 
way with the ultimate reality. Knowledge is not a passive recep- 
tion of impressions (Kant argues), but an active assimilation of 
them under concepts,—the mind is not a blank sheet, but a 
working organic whole with a structure, — and so knowledge is 
confined to appearances, which are the products of the under- 
standing at work with concepts on the materials of the senses. 
Thus the objects of knowledge form a neat and orderly closed 
system through which the wind of reality does not blow. The 
safe and sheltered island mapped out by thought is untroubled 
by the waves of the ding-an-sich which beat along its shore. 
Why must this strange introversion go with the notion that 
the mind is active in knowledge? Granted that thought works 
with concepts and categories, that the mind is not like a vat of 
dough, merely receptive to external impressions, but that it does 
something in cognizing an object. Still, it does not follow that 
this activity is a contraction of the mind within itself. The con- 


276 SYMBOLISM AND TRUTH 


cepts along the grooves of which cognition is directed may lead 
the mind outward to a more complete knowledge of the real, 
rather than twist it inward upon itself. The more reasonable 
corollary to the observation that the mind is active in cognition 
is the exact opposite of mind-isolation. The activity of thought 
through concepts, intentions, (that is, symbols with their atten- 
dant mental attitudes), should bring the mind into more perfect 
and stable relations with the reality it touches in “the original 
receptivity of the senses.”’ We cannot conclude that the organ- 
ized knowledge of perception and experience is not knowledge of 
realities simply because thought plays a part in the organization. 
If reality itself is a complex whole, with “a time-less subtlety 
of complexity,” ! surely it is not strange that reality should be 
clearly apprehended only by an organized and active mentality. 
What is needed in place of the Kantian theory of isolation is the 
notion that mind by its activity joins itself to real things in 
knowledge, that is, an epistemological monism which takes ac- 
count of thought-activity in cognition. Mind grows into a cog- 
nitive unity with the reality it originally knows only in fleeting 
and momentary glimpses; the mind in knowing is actively con- 
tinuous with real objects. We shall presently say more of this 
continuity. 

Kant’s tidy world of experience, created by the mind at work 
with concepts and categories, could be peopled only by objects 
for which these concepts and categories are universally and nec- 
essarily true; and so necessity is brought into connections of 
“matters of fact” (as against Hume) at the cost of severing the 
whole world of fact from a vast and incomprehensible realm be- 
yond fact. One feels cheated, tricked, by this vindication of a 
priori knowledge. It is a peace without victory. And what of this 
theory of mind-creation itself? Is it, too, nothing but a mind- 
creation? If not, Kant is thrown back on the insight into real- 

1 A. N. Whitehead, The Principles of Natural Knowledge (1919), p. 15. 


THE METAPHYSICS OF KNOWLEDGE Q77 


ity of which Aristotle and Spinoza speak. Kantianism is slain by 
its own hand unless its own first principle — that knowledge 
cannot go beyond appearances — is apprehended as not itself 
an appearance, apprehended by a kind of reason not subject to 
the limiting categories of ordinary thought. But to admit such a 
rational insight or “intuition” would have been a return to dog- 
matism of the sort Kant hoped forever, by a dogmatism peculiar 
to himself, to demolish. 

Kant’s “dialectical” arguments attempt to show the futility 
of offering rational answers to metaphysical questions. But the 
cure is more reason, closer analysis, clearer concepts, and not, 
as Kant would have us believe, the surrender of rational meta- 
physics. A growing knowledge is bound to meet contradictions 
and thus to alter its concepts, and here lies the correction for the 
Kantian antinomies as well as for the more numerous contradic- 
tions which Mr. F. H. Bradley — following the scent of the dia- 
lectical argument even further than Kant — finds, in his Ap- 
pearance and Reality, to be inherent in discursive thought. This 
much truth can be distilled from both the Kantian and the 
Bradleyan dialectic: it is fatal to employ the concepts of the 
special sciences for unscientific, that is to say, for metaphysical 
purposes. Metaphysical categories (if there are any such) must 
be the widest possible categories. Mr. Bradley finds that thought 
in the effort to complete itself does not attain to wider concepts, 
but “commits suicide” by transcending its own forms, thus 
making way for the dim apprehension of an Absolute of which 
discursive knowledge gives only an imperfect and restless fore- 
sight. In this way Mr. Bradley escapes agnosticism to fall into 
something very close to mysticism. Kant’s conclusion from his 
antinomies is, on the other hand, the most glaring and insoluble 
antinomy of all. An inherently defective reason becomes able to 
know its own defects; a mind isolated from reality and confined 
to a world of phenomena becomes negatively but not positively 


278 SYMBOLISM AND TRUTH 


aware of its isolation. Even so the mind craves a positive knowl- 
edge of this reality and its relation to the world of experience. 
The noumena do not cause phenomena, for causation is a con- 
nection between objects of experience only. Indeed, theconclusion 
ought to be that the noumena are not related to the phenom- 
ena, for relations hold only between phenomena. The thing-in- 
itself, the ultimate reality thus severed from its appearances, is 
an entity which plays the same part in knowledge as zero in 
arithmetic; the addition or subtraction of it does not alter the 
value of the other elements. The outcome of the Kantian“ dia- 
lectic” is that knowledge of that which limits knowledge is 
negative only; which amounts to saying that knowledge is 
limited in a way that is not known by something that is not 
known. And it is a short step to the conclusion that knowledge is 
not limited, and hence to a rejection of the whole theory of 
mind-isolation. 

One other conclusion stands out in the “dialectic.” Reason is 
always attempting to complete the synthesis of experience, to 
effect a “complete unity of knowledge . . . by which that know]l- 
edge becomes not only a mere aggregate, but a system con- 
nected according to necessary laws.’ Kant sees reason as dy- 
namic and directed toward a goal, which it approaches but does 
not reach. Not content with a slow process of growth and cor- 
rection, it takes disastrous short-cuts, falling thus into self- 
contradiction. But this incompleteness of knowledge is not a 
sufficient ground for the agnostic separation of appearance from 
reality. It is one thing to assert that knowledge at any particu- 
lar time does not give us the whole of reality. This is a mild con- 
fession of ignorance and finitude, a gentle and tolerable agnosti- 
cism, which is the part of intellectual humility in the face of 
changing concepts, shattered theories, and discredited beliefs. 
It is quite another thing to assert that knowledge never grasps 
more than an appearance. A knowledge that is not complete in 


THE METAPHYSICS OF KNOWLEDGE 279 


detail must nevertheless reach through to reality; otherwise, it is 


not knowledge. 
IV 


Four major points emerge from this discussion of agnosti- 
cism. (1) Any final criticism of the validity of knowledge must 
rest on metaphysical premises. The epistemological tradition 
which pretends to determine the limits and extent of human 
knowledge — especially, whether metaphysical knowledge is 
possible — appeals itself to metaphysical premises which are 
true without limitation. Appearance and reality cannot be held 
_ apart. (2) Though the mind is active in cognition, this fact need 
not lead to the conclusion that the mind shuts itself out from 
reality, building a world wholly its own. To the theory of mind- 
isolation must be opposed that of the continuity of the mind 
with real objects in the act of knowledge. The activity of the 
mind in the channels of concepts brings it into more complete 
touch with the reality of which sensation gives only passing 
glimpses. Through the use of concepts knowledge expands out- 
ward to reality, rather than inward to its own ideal world. (3) 
At every moment knowledge is incomplete, the whole of reality 
is not known in detail; the truths of to-day may be reversed by 
those of to-morrow. Yet the very notion that knowledge is in- 
complete demands that some knowledge be ultimate. Thus (4) 
a rational insight or intuition is needed to take account of meta- 
physical truth, for the truths that vindicate (or enable us to 
repudiate) all others cannot themselves be vindicated or repudi- 
ated, nor can they be merely postulated. They must be appre- 
hended as final. 

These conclusions must be expanded and correlated with the 
description of knowledge previously given. 


280 SYMBOLISM AND TRUTH 


V 

The essence of the first point is this: if there is any knowledge, 
there is knowledge of reality. An appearance is never a bare ap- 
pearance, for if it is true that it is an appearance, then it has 
some status in reality. It is really an appearance. The opposi- 
tion between appearance and reality becomes less and less sig- 
nificant the more one contemplates it. The question is, not 
whether what appears is a reality, but what sort of reality it is. 
What is its place in the scheme of reality? An appearance de- 
ceives when it is misplaced in reality or judged to be all there is, 
yet even a deceptive appearance is something; it cannot be dis- 
missed as not being. To hold that appearances have no reality is 
to deny that they are appearances, and hence to wipe them, and 
all the problems connected with them, clean off the slate. If the 
distinction between appearance and reality is to have a mean- 
ing it must fall within experience, and not between what is 
known and what is unknown or unknowable. It must fall within 
an apprehended reality. The very terms “appearance” and 
“reality” mislead one. We ought not to say that the reality we 
know differentiates itself into appearances, but into parts, 
aspects, elements, modes, which never lose their essential real- 
ity. What we call “appearances” are fragments of reality, and 
reality is in the fragments no less than in the complex structures, 
that is, objects, situations, facts, into which these fragments 
fit to form a world. 

The task of metaphysics is to describe what is most general 
(and hence least noticeable) in this apprehended reality, how- 
ever fragmentary the part apprehended may be. Metaphysics 
cannot look for the real beyond or behind experience, nor in an 
ideally complete experience. It must, like any other effort to 
think clearly, dig into the basic units of knowledge which are 
presentations or wholes of experience. Metaphysics is the most 
searching possible analysis of these wholes. 


THE METAPHYSICS OF KNOWLEDGE 281 


This analysis should reveal what part the mind plays in ap- 
prehending these wholes. Does the mind in some far-reaching 
sense create their reality? Or do they in some mysterious way 
enter the mind from outside and mold it to their own forms? 


VI 


There has always been a tendency to break up the act of 
knowledge into sensation and thought, sensation being passive 
and thought active, and this has led to curious results, some 
of which have already been observed. In the main, those who 
have stressed sensation and the passive réle of mind have in- 
sisted that reality is external and indifferent to mind, and that 
reality becomes known through impressing itself on the mind; 
while those who have stressed thought have made the opposite 
claim — that reality is mental, rational, a thought-creation, and 
that it is known through the mind’s activity. There is something 
to be said for both of these views for the reason that the act of 
knowing is not sensation with thought added, or thought with 
sensation entering accidentally in it. To know is to be at once 
active and passive, to receive an impression and reflect upon it. 
The act is a single whole in which thought and sensation are 
blended; what is impressed on the mind is assimilated to, and 
not distinguished from, what is meant, imagined, thought. Con- 
crete knowing is the active assimilation of reality through sen- 
sational-thought. We have spoken of this before as presentational- 
thinking. It is impossible to say where the receptivity of the 
mind leaves off and its activity begins. Certainly it is highly 
artificial to draw this line at sensation, for there is no such thing 
as a pure sensation in abstraction from the cognitive act as a 
whole. As an element within this whole, sensation or sensing no 
less than thought is active. Moreover thought, as an element 
within the cognitive whole, has its passive side; it comes 
sharply against the thing it means given in experience, and 


282 SYMBOLISM AND TRUTH 


this encounter checks and at the same time fulfills its inten- 
tions. 

What has been previously said of thought must be recalled: 
that thought is essentially reference through symbols, an out- 
ward reach of the mind toward objects. There is a distinction 
between pure thought, which is reference and nothing more, and 
perceptual thought — which is reference when what is referred 
to is also immediately presented. The latter is what we are now 
speaking of as “concrete knowing.” This is the basic form of 
knowledge. Pure thought, purely mediate knowledge, is knowing 
in which the element of presentation (that is, passivity) is re- 
fined away, so that the thing meant is no longer given but merely 
intended. I do not know the other side of the moon concretely, 
but I do know concretely the facade of the house opposite upon 
which my window looks. Since pure thought is a distillation, an 
abstraction, from concrete thought, it is to the latter that we 
must look for the fullest relation of the mind to real objects in 
knowledge.! 

The view that objects impress themselves on the mind 
through the senses is insufficient for many reasons. Sensations 
are nothing in themselves; they are always parts of larger 
wholes. It is not correct to say that we “sense” relations, facts, 
complex structures; yet we experience these things. Cognition is 
always recognition; memory plays a part in it, and what is given 
has a reference before and beyond itself. There is an adjustment 
to experienced objects; they are classed, catalogued, fitted into a 
scheme of things in the very act of perception. The fact that 
objects are experienced as “black,” ‘‘white,” “round,” or even 
as “objects” or “‘sense data,” shows that a concept is actively 


1 This distinction between pure and concrete thought corresponds to 
Aristotle’s distinction between potential and actual knowledge. In actual 
knowledge we grasp the real; potential knowledge needs something, a fulfill- 
ment or realization, to become actual knowledge. See W. D. Ross, Aristotle 
(1924), p. 171; also Aristotle, Metaphysics, Bk. XIII (M), ch. 10. 


THE METAPHYSICS OF KNOWLEDGE 283 


at work in the apprehension of them. Unless objects can be con- 
sistently assimilated to the knowledge already present to us, 
they puzzle us; we feel that they are not clearly apprehended, 
that we have not yet succeeded in perceiving them. Thus not 
only is a single concept present in the apprehension of objects, 
but a whole body of theory — certainly the whole body of com- 
mon sense — presses forward to enter into the act of knowing, 
and the perception remains unstable until it is reconciled with 
this body of knowledge. All these and many other arguments 
point to the inadequacy of the notion that knowledge is a pas- 
sive reception of impressions. Concrete knowing feeds on the 
whole of knowledge; what has been experienced, and the use the 
mind makes of it, determines what is and will be experienced. 
The direction of one’s thoughts, meanings, intentions, codperate 
in what he sees and hears, no less than does the external situa- 
tion in which he happens to find himself. If the mind were a 
tabula rasa, there is no reason why first impressions should not 
be as clear, as complete and final, as last impressions. 

Yet there is a stubbornness, a resistance, an alien character, 
in the objects of concrete experience which prevents us from 
taking the opposite point of view, namely that they are thought- 
creations, things merely meant and in no sense given. We do not 
invent the things we see about us; they force themselves in upon 
us, and though the mind goes forth through its intentions to 
meet reality, still thought comes in the end to something un- 
yielding. If experience deceives us, we do not get rid of the ex- 
perience by apprehending it under proper categories and thus 
doing away with the deception. The data remain, however we 
conceptualize them. It is impossible to convince one’s self that 
the world is merely a coherent set of meanings. Whatever the 
activity of thought does in contributing to concrete knowing, 
there always remains a matter not its own creation. However 
thought may elaborate this matter, the matter persists, to con- 


284 SYMBOLISM AND TRUTH 


fine and complete concrete thought.! Of the infinity of worlds 
possible to purely abstract thought, one is realized, and it is this 
one which experience reveals to us. For abstract thought alone 
any other world might equally well have been. 

The idealist, who looks on reality as a rational system of 
meanings or concepts, still finds it necessary to account for the 
stubborn givenness of this world; he cannot ignore the specific 
materials of knowledge; he must make it clear why this rather 
than that possibility is realized. And quite properly, not wishing 
to fall into the Kantian predicament, which places reality be- 
yond the reach of hought and yet maintains that in some 
strange way this reality limits and molds experience, even 
though this experience is always of ideal (mental) objects only 
—not wishing to fall into this difficulty, the idealist distin- 
guishes between subjective and objective thought, between 
relative and absolute knowledge. Finite experience is a frag- 
ment of the absolute experience, finite thought a part of the ab- 
solute thought. Through entering (partially) into this absolute 
thought, we know reality, and so the world about us is more 
than the creation of our own minds. 

This idea is most simply put by Berkeley, who interpreted 
the whole of nature as a direct communication from God. In the 
hills, the trees, the stones, the events of history, we read the 
thoughts of the Deity; all are signs of what is passing in His 
mind, The stability of nature, the persistence and externality of 
perceptual objects, arise from the stability, persistence, and ex- 
ternality of God’s thought. Illusion and error are man’s dream; 
truth is the apprehension of what God compels us to know. 
Berkeley’s idealism has a fresh, naive beauty not found in his 
more sophisticated brethren, the Post-Kantians; but in essence 
it is absolutism. 

Absolute Idealism, then, does not do away with the alien qual- 


1 Matter in the Aristotelian sense. 


THE METAPHYSICS OF KNOWLEDGE 285 


ity of the objects of experience, and at the same time it takes 
complete account of the work of thought in apprehending these 
objects. It does not ask us to believe that reality stamps itself 
on the mind from outside, that we are mere receptacles of im- 
pressions and ideas. Knowing becomes an entering into reality, 
a sympathetic understanding of a thought-world which is alien 
to and more inclusive than our own world of thought. The ac- 
tivity of the human mind is compelled and illuminated by the 
activity of the Absolute Mind in which it has its being. 


f 


VII 


This is a heady doctrine, and one pauses to ask himself what 
it comes to. What is the Absolute Mind? Need one call it a 
“mind” ? What significance remains in speaking of reality as 
essentially “thought”? 

The chief argument for idealism, aside from the necessity of 
accounting for the mind’s activity in knowledge, is one that has 
been mentioned above; the mind must be continuous with the 
reality it knows. Thus it is easy to leap to the conclusion that 
reality is mental, to Berkeley’s esse est percipi. Yet objects re- 
fuse to be reduced to my mental states or my meanings; they 
persist, I believe, when my back is turned (and certainly Berke- 
ley also believed this). The laws of nature, of mathematics and 
logic, are not my thoughts; I discover and do not invent them. 
And though Berkeley would have admitted that he “ate, drank, 
and was clothed with ideas,”’ these were God’s ideas and not 
his own. Reality must be sufficiently close to the mental to be 
known through the activity of my mind, but it must not be so 
completely mental as to be reduced to this activity. The ideal- 
ist’s argument comes to this: he is forced to distinguish “men- 
tal,” from “mental ,”, and what remains? Merely lip-service 
to a word. What he is saying, apart from this word “mental,” 
is that his mind is so related to reality that it can know reality 


286 SYMBOLISM AND TRUTH 


through its activity. Obviously, no mind can be completely 
foreign to the reality it knows; the mind and its objects must be 
in the same universe; they must not be so wholly sundered that 
no relation, no sort of community or continuity, can exist be- 
tween them. But it profits me nothing to insist that this reality 
is mental, a thing of thought. I mean that it is “mental ,” and 
not “‘mental,” and these are very different. 

“Reality”’ is the most inclusive of all possible terms; if any 
distinctions of meaning exist, these must arise within reality. 
There can be no significance in defining reality in one way rather 
than another, for whatever special term be taken as its defini- 
tion, this term will have arisen as a distinct “‘somewhat”’ within 
reality, and it will lose its special meaning if it is made equiva- 
lent to reality. To speak of reality as mental is to spread mental- 
ity so thin that, to all intents, it becomes “‘not-mental.’’ We are 
driven to qualifications — “‘objectively”’ and “‘subjectively”’ 
mental — to bring back the significance that has departed from 
the term. 

One might as well recognize at once that reality is reducible 
to none of its aspects or modes, and be content with the term 
“‘reality”’ in its simplicity as undefined. For the logic of the 
situation will finally force him virtually, if not explicitly, into 
this position. The realist declares that “reality is independent of 
the knowing subject and not essentially mental, though it can 
be known”’; the idealist — what appears to be the same thing — 
that “‘reality is mental (but not subjectively so) and dependent 
on mind (but not on the subjective mind).’”’ Both agree on the 
fundamental point that the mind in knowing is continuous with 
real objects; both repudiate the Kantian dualism of idea and 
real object, of phenomenon and thing-in-itself. In this respect 
the American realists go further than many idealists; they assert 
not merely that the mind is continuous with the real objects it 


THE METAPHYSICS OF KNOWLEDGE 287 


knows, but that it is identical with them — or at least partly 
so. 

The truly significant tendency in modern metaphysics, 
whether it be idealistic or realistic, is toward breaking through 
the old fixed categories of the mental and the physical. We are 
returning to the point of view of the ancients, having suffered 
for three centuries from the blindness of the Cartesian dualism. 
If a chasm is opened, as it was by Descartes, between the physi- 
cal and the mental, there is no way of closing it. We have strug- 
gled vainly throughout most of modern philosophy to solve a 
problem which, as it is stated, is insoluble: that of the relation 
of “thinking substance” to “extended substance.”’ In psy- 
chology it has appeared as the mind-body problem: How can a 
physical thing be related to, act upon, control or be controlled 
by, a non-physical thing? And there is no answer in terms of the 
Cartesian concepts. The theory of psycho-physical parallelism 
merely restates the problem in a more vivid way. Psychologists 
have learned that they must go back to earlier notions and 
merge “body” and “mind” in larger concepts such as “‘struc- 
ture” and “‘function.” Mind and body are aspects of, abstrac- 
tions from, a known reality which is wider and richer than either. 
In the theory of knowledge, the dualism of the mental and the 
physical has led to that extraordinary difficulty — how can one 
know the physical world? — a question which, rightly, did not 
enter Aristotle’s head. Descartes solved it by a tour de force, 
but it would not have needed to be solved unless he had assumed 
that physical objects are so completely disparate from minds, 
so wholly resident in another universe, that nothing short of a 
miracle could bring them together. Physical objects are not so 


1 See E. B. Holt, The Concept of Consciousness (1914), chs. 8, 9. Mr. Nor- 
man Kemp Smith’s recent Prolegomena to an Idealist Theory of Knowledge 
(1924), points out that the idealism, realism, and naturalism of current philos- 
ophy are indistinguishable on many fundamental issues. 


288 SYMBOLISM AND TRUTH 


foreign to minds that they cannot be known, nor are they so 
akin to minds that they cannot be when they are not known. 

This is what both idealists and realists recognize, that the 
knowing relation is an entrance of the mind into external ob- 
jects, or an entrance of external objects into the mind — which- 
ever way one chooses to put it. 

Idealism as it appears in Berkeley is a polemic against ma- 
terialism rather than against realism.! In his day materialism 
was showing its head everywhere, and the good Bishop of 
Cloyne wished to refute a doctrine against which all that has 
been said above concerning idealism can be equally well main- 
tained. To speak of reality as “‘matter’’ is to divest the term 
“material”? (or physical”) of its specific meaning; for within 
this so-called ‘‘material” reality mind arises, at least as an epi- 
phenomenon—a shadowof a shadow of matter. And this subtler 
thinking matter is no less a reality than the cruder unthink- 
ing matter. We have “matter ,” and “matter,.” Thus “real- 
ity,” following the inevitable logic of the meaning of this term, 
widens out and transcends its physical as well as its mental 


aspect. 
VIL 


The capital crime of metaphysics is the attempt to reduce re- 
ality to one of its aspects or modes, a crime which is equalled 
only by its converse — the attempt to sever reality from all of 
its aspects or modes. Reality is fuller than any single set of rela- 
tions, laws, principles, which can be discovered within it. It is all 
these, and more. But though it is not possible to define reality 
— to state exhaustively in conceptual terms exactly what it is to 
be real — there are perfectly general truths which hold without 
qualification for reality. Any one who believes that a rational 

1 We mean “realism” in the modern rather than the mediaeval sense. 


Berkeley’s repudiation of abstract ideas can certainly be construed as a 
polemic against the realism of the schools. 


THE METAPHYSICS OF KNOWLEDGE 289 


metaphysics, or for that matter rational knowledge, is possible 
must believe that there are such general truths. The terms in 
which these truths are stated must be sufficiently wide to include 
both the mental and the physical; they must spring from the 
observation that reality is neither physical nor mental exclu- 
sively, but that it can be both. The physical and the mental 
must be capable of fusion. Further, it must be recognized that 
the dichotomy of the physical and the mental does not exhaust 
reality, but that there are other orders of being — perhaps, as 
Spinoza thought, an infinity of such orders.! 

No metaphysics can successfully maintain that reality is 
~ essentially disparate from mind. Non-mental objects must be 
capable of coming into the knowing relation, and hence there 
must be unities which include both the mental and the non- 
mental. Nor can a metaphysics maintain that reality is essen- 
tially internal to mind in any significant sense of the term 
“mind.” “Idealism” and “spiritualism” suggest the latter 
point of view, while ‘“‘realism,” by a modern perversion of its 
meaning — by stressing the externality of terms and relations, 
of mind and its objects, and forgetting that all relations also en- 
ter into and modify their terms — suggests the former. There 
should be a name for the metaphysics which consciously repudi- 
ates both of these points of view and sets out from the notion 
that reality is an unbroken whole whose parts mutually if not 
completely determine one another, the mental and the non- 
mental being phases within this whole. Our answer to the 
question — how is the mind related to real objects in the act’of 
knowledge? — rests then on this premise, that reality is neither 
essentially disparate from or internal to mind. Concrete knowl- 

1 Mr. A. N. Whitehead’s recent lectures at Harvard have, for the present 
writer, thrown a wholly fresh light on metaphysical problems; especially on 
this question of how, in detail, a set of general concepts can be framed which 


embrace the physical, the organic, the mental, and at the same time leave 
room for other orders of being. 


290 SYMBOLISM AND TRUTH 


edge is first of all knowledge of the real, and only secondarily 
knowledge of the mental or the physical. Within this appre- 
hended reality, two orders can be distinguished, the mental and 
the physical, but the one is no more essentially real than the 
other; each is a mode of reality, bearing on itself the stamp of 
being. 

Furthermore, the act of knowing has both its passive and ac- 
tive side; here as in physics the law of action and reaction ap- 
plies. The mind receives an impression and correlates it with 
other impressions, fits it under concepts, actively assimilates it 
to the whole body of knowledge. Objects are perceived through 
thought and thought through perception, for as Kant’s phrase 
runs, ‘percepts without concepts are blind, and concepts with- 
out percepts are empty.” Yet the activity of thought, rather 
than estranging us from external reality, brings us into contact 
with a reality other than thought. 


1X 


Let us examine more fully what is meant by the “mental” 
with a view to showing how the mental can be continuous with 
the non-mental in cognition, and why thought-activity is needed 
to put us in touch with objects. 

Forget as completely as may be the distinction between the 
physical and the mental; put yourself in the most naive possible 
frame of mind and gaze on the things about you. What you see 
before you is a field of objects, probably a changing field; you 
close your eyes and see other, fainter objects, or perhaps only a 
dark area illuminated by dim streaks of light; you open your 
eyes, and perceive objects closely if not indistinguishably like 
those you first saw; and all the while within your body you ex- 
perience faint or vivid sensations of movement, perhaps of pain 
or of a vague well-being. There is no reason for singling out any 
part of this whole experience as mental. Some parts of it are 


THE METAPHYSICS OF KNOWLEDGE 291 


more closely associated with the body than others; the pain is 
localized in the body, while the wall of the room is not; but ex- 
ternality or internality to the organism gives us no criterion of 
the mental. 

The distinction is certainly not an early datum of experience; 
it comes to the surface only after reflection, only after certain 
sequences and orders of events have been observed. Then it is 
discovered that some of the things experienced hang together 
by a different sort of coherence from others. Within the single 
field of real objects, which is the original cognitum, we find two 
worlds which differ in structure but easily become a single 
world, and there can be no question as to how knowledge passes 
from the one to the other. From the beginning knowledge is 
synoptic, it covers both. 

The lineage of this view, which was strikingly put by William 
James in his essay, Does Consciousness Exist,’ can be traced at 
least to Spinoza: “‘thinking substance and extended substance 
are one and the same thing, which is now comprehended through 
this and now through that attribute.” *? James need only have 
added to the two types of structure found in the world of “pure 
experience,” an infinity of types of structure (corresponding to 
the infinite attributes) to have become a thorough-going Spino- 
zist. Mr. Bertrand Russell, who has elaborated James’s view, 
as distinguished from 


’ 


gives the name ‘‘mnemic causation,’ 
“physical causation,” to the type of law which is characteristic 
of the mental realm.® 

Memory is certainly one of the chief principles of order in the 
mental world, but the term “‘mnemic causation” is too sug- 
gestive of Hume. Its effect is to turn the attention away from 
the very essense of mind, activity toward an end — the unity of 

1 W. James, Essays in Radical Empiricism, 1912. 


2 B. de Spinoza, Ethics, Bk. II, Prop. VII, note. 
3 B. Russell, The Analysis of Mind (1921), sect. 4. 


292 SYMBOLISM AND TRUTH 


memory and purpose, of backward and forward looking inten- 
tions, which is a personality or self. If the soul-substance view of 
mind is dead, so also is that of Hume — that the mind is a stage 
where ideas pass and repass without a spectator to take account 
of them. The stuff of “pure experience” does not combine and 
recombine of its own weight, according to the principles of asso- 
ciation or of mnemic causation, to form a mind. The laws of 
mind are laws of purposive activity; memory is itself an activ- 
ity; will, striving, conation, are at the core of mind; and these 
strands of activity are always caught together in a unity which 
is the self of the moment. This self changes, but not without per- 
sistence of its structure. At any moment a definite past, which 
can be called up and known again (though not exactly as be- 
fore), converges toward the present, and a future — purposed, 
desired, intended, striven for — expands from the present. This 
is a mind. 

Moreover, the activity of the mind can become reflexive, it 
can be turned upon itself or its own products; and this “‘reflec- 
tion” occurs in two very different ways. (1) In desiring, we know 
that we are desiring; in knowing, we know that we are knowing. 
Josiah Royce speaks of this as the “self-representative”” power 
of knowledge,! that is, knowledge can reflect on its own proc- 
esses. (2) The activity of the mind tends also to crystallize into 
a content which is still wholly within the mind. To think of or 
intend something is to set in motion the whole apparatus of 
cognition; the thought refuses to continue merely as a pure 
intention but strives to become concrete, that is, to fulfill itself; 
and thus an image or “reflexive content” appears. The image 
is a deposit of the activity. To know the image is therefore 
not merely to know that we are knowing; it is to be aware of 
something the mind creates. Images are the products of minds 
rather than minds themselves; they arise in the process of 


1 J. Royce, The World and the Individual (1901), Vol. II, pp. 509 ff. 


THE METAPHYSICS OF KNOWLEDGE 293 


mental activity, but they are not the activity, nor are they of 
the same stuff as non-mental objects. Though the activity of 
the mind creates reflexive contents, there is no foundation for 
the belief that all experience is of reflexive contents only; and 
if this is the meaning of Locke’s statement that “knowledge 
is conversant only with ideas,” an essential fact’of knowledge is 
overlooked, that one knows ideas and the mind that creates 
them only by distinguishing them in a reality which extends 
beyond both. 

Given, then, that the mind from the outset knows something 
other than itself, and it still remains to be shown how the mind 
is continuous with this non-mental reality in cognition. 

This continuity is not identity. The mind is other than the ex- 
ternal reality it knows; there is always more of the reality to be 
known, and always the knowing, which is of the mind but not 
the same as the non-mental object. (The knowing tends also to 
create a reflexive content which fuses with the non-mental 
object, but, difficult as these images are to distinguish from 
the object, they are not identical with this object.) The epis- 
temological monism which identifies mind with its non-men- 
tal objects makes the object of knowledge a sponge that ab- 
sorbs everything — error and illusion, as well as meaning and 
truth. 

Mind is cognitively continuous with non-mental objects in 
the same general sense as other things in this world are continu- 
ous with one another. And we are not speaking here of the math- 
ematical theory of continuity, but of something found in experi- 
ence, which M. Bergson describes as “interpenetration” and 
Mr. Whitehead as the general ‘“‘togetherness’’ of objects and 
events. This continuity is not, we believe, a relation. It is rather 
the unity or wholeness within which both terms and relations 
arise. Distinct things singled out as self-identical always merge 
in the wholes within which they are distinguished, and this union 


294 SYMBOLISM AND TRUTH 


of the parts in the whole is not due to confusion in the perception 
that distinguishes them, but to the nature of reality. Though 
reality at all points takes on distinct structures or forms, these 
structures are always elements in wider structures, and every 
whole is continuous with other wholes. 

Let us recall what was said previously in connection with 
relations| A is related to B not because the relation R which 
unites A and B is related to its terms, for if this were so an in- 
finity of relations would be needed to bring about a unity of the 
terms. The terms and relation are joined once for all. They form 
a whole in which the aspects A, B, and R can be distinguished; 
this is what we mean by saying the relation R holds between A 
and B. There is no point where the relation ceases to be a rela- 
tion and becomes a term, or where the terms cease to be terms 
and become a relation. Motion is an apparent case of such con- 
tinuity. There is no point at which the moving object ceases to 
be in one place and passes into another; in fact, the passage is 
just a continuous process which cannot be completely described 
in terms of places or points, any more than a relation between 
terms can be described in terms of elements and a relation. We 
must have the ultimate concept of the unity of the elements. We 
must think of the elements as abstracted from this unity, in- 
stead of thinking of the unity as added to the elements. We must 
think of the points and instants, in terms of which we describe 
the motion, as abstracted from the passage, rather than of the 
passage as superimposed on the points and instants. 

The mind and its objects fuse as one segment of a motion 
fuses with another, as a relation merges with its terms, as any 
part of a whole or any whole, with another. The mind projects 
itself into the non-mental and the non-mental into the mind. 
There is an unbroken flow of process, and throughout a stretch 
of this process—at the segment of “greatest luminosity ’’—the 


1 See above, ch. III, sec. vii. 


—— sO 


THE METAPHYSICS OF KNOWLEDGE 295 


cognition of the object comes into being. Minds are together 
with external objects in the same general way as objects, events, 
situations, are together with one another. 

This continuity of mind and its objects needs, however, to be 
further specified. Continuity (or unity) is a general background 
against which any elements of reality — whether they be minds, 
physical objects, or what not — stand out; and in each distin- 
guishable whole of experience this continuity is of a specific sort. 
Thus the whole (ARB) might be a whole of “spatial before- 
ness”, that is, it might be the fact “A is before B in space.” 
Motion is obviously a spatio-temporal unity of a specific kind. 
_ What sort of unity or continuity is this cognition of a non- 
mental object? Certainly it is not a spatial continuity. Though 
the object known may be spatial, the cognition is not in space 
but of space. These two types of whole —the spatial and the 
non-spatial — come together in the wider whole of cognition. 
On the other hand, the continuity of mind and its non-mental 
objects is both zn and of time; the mind as well as the world it 
cognizes is a changing, temporal unity. In the specious present 
of knowledge we grasp, in an act which is itself temporal, the im- 
mediate past and future of the thing known, so that each whole 
of cognition — being itself in time — is nevertheless a survey of 
time. And yet the object of knowledge has its non-temporal 
aspect. It is a “‘what,”’ a universal as well as an individual, and 
its “what” cuts across time as well as across space and belongs 
intrinsically to no single time or space. This is indeed the great- 
est paradox of knowledge, that being in time it takes hold of 
both the temporal and the non-temporal. The key to this para- 
dox is memory. In so far as we attain to any knowledge of uni- 
versals, of timeless objects, we do so through memory; and 
since concrete knowing is always the seizure of something both 
universal and individual, of something unique and passing which 
is nevertheless blended with something that has been and may 


296 SYMBOLISM AND TRUTH 


be again — for this reason, concrete knowing is a continuity of 
a remembered past with a new, yet familiar present. 

The passage of thought is plainly not motion, though it is 
activity; and one speaks only metaphorically of the mind as 
“going forth to meet its object.” Knowing is a fulfillment, a 
realization, in which the mind attains an end which has been 
obscurely before it; and whether or not teleological categories 
are of use in describing nature, they are indispensable in describ- 
ing mind. 

Finally, the act of knowledge is inclusive of itself. In knowing 
objects we know the process by which we know, the mind re- 
veals itself through its commerce with its non-mental environ- 
ment. And beyond all this, knowing has its peculiar tang which 
is no more subject to description than the sound of a tonic triad 
or achord of the seventh. Analysis discerns in knowing, as in the 
chord of the seventh, a number of phases, but it still remains 
simply what it is — a unique union of mind and object. 


xX 


It must not be supposed that the external objects which pro- 
ject themselves into knowledge are those that act on the senses. 
We perceive colors, shapes, smells, sounds, motions, houses, 
trees; we observe relations between these objects and laws that 
hold for them; but we do not perceive light-waves or sound- 
waves, molecules, electrons or electronic structures, nor do we 
perceive the bodily processes which light-waves or sound-waves, 
molecules or electrons, arouse in us. One can construct a theory 
of how these infra-experiential entities act on the sense-organs, 
but it is not possible to perceive these entities through their ac- 
tion on these organs. 

An immense amount of error has been propagated by the 
view that the only real physical objects — or, for that matter, 
the only real objects — are these infra-experiential entities in 


THE METAPHYSICS OF KNOWLEDGE 297 


terms of which physical theory is constructed. The problem of 
our knowledge of physical reality is totally misconceived if one 
attempts to solve it by explaining how these entities, which are 
undoubtedly connected in some way with our sensory reactions 
and with all our intellectual processes, can be known through 
this connection. Whatever the relation of these entities to men- 
tal processes may be, it is certainly not the cognitive relation. 
This must be sought elsewhere. 

The physical objects of concrete knowledge must be distin- 
guished from the physical objects of scientific theory; these two 
types of physical object together make up the complete physi- 
cal object. There is no doubt that perception penetrates only a 
short way into the complete physical object; what is perceived 
must be pieced out by a theory as to the nature of this whole 
object. But this lack of concrete knowledge of the whole physi- 
cal object does not make the objects of perception purely men- 
tal. They retain their otherness, they still belong to an order dif- 
ferent from that of mind. The presented physical object is a 
mediating link between the mind and the physical object of sci- 
entific theory. It is sufficiently like the mind’s reflexive content 
(images, dream-perceptions, etc.), to be deceptive when taken 
out of its setting. (There is no intrinsic difference for perception 
between an isolated physical sound, for example, and an isolated 
sound-image.) Yet the presented physical object, in its setting, 
bears the marks of a structure different from that of the mind or 
the mind’s reflexive contents; and it is on this observed differ- 
ence of structure that a theoretical world of physical objects, 
extending completely beyond concrete knowledge, is built. In 
the act of cognition, we are aware at once of the distinctness and 
the unity of our minds with the presented physical object; but 
we are never concretely aware of how this perceptual object, or 
the mind, is related to the scientific physical objects. A color is 
doubtless vastly unlike a light-wave, yet the color is a physical 


298 SYMBOLISM AND TRUTH 


phenomenon, a non-mental reality. It comes into being in a cer- 
tain situation, theoretically represented as a light-wave striking 
an eye. It is a part of the whole physical situation of which the 
light-wave is a part; it is that part of the situation which can be 
in knowledge and at the same time in the external world. 

The problem of how the objects of physical theory are related 
through the presented physical objects to the mind, of how 
these three can be together, is a phase of the problem of mind 
and body. But the problem of the cognition of the physical 
world, or for that matter of any order of being beyond our own 
minds, is wholly another question. If there is to be any physical 
theory and any problem of mind and body, both the physical 
and the mental must be known. The mind could not leap mirac- 
ulously to the notion of an infra-experiential world of atoms and 
electrons and then ask, ‘“‘What is the relation of this world to 
the mind?” Whatever the solution to the mind-body problem 
may be, the mental and the physical are continuous in a specific 
way in cognition. They must also be continuous in some other 
specific way through the action of molecules, electrons, light- 
waves, on the nervous system. 

Since the presented physical object arises in a situation in 
which both a mind and other physical objects, not presented, 
codperate, one can ask — what aspects of the presented object 
are relative to this situation? — and what aspects extend be- 
yond it? 

These questions can be generalized for any situation. Every 
situation is altered in general complexion if some of its elements 
are removed. Something more than these elements goes out of 
existence; the original “‘what”’ of the whole is extinguished and 
the remaining whole is a new “what,” perhaps of a very differ- 
ent complexion. Thus there is something in every situation 
which is relative simply to that situation. Take away the spires 
of the cathedral at Chartres and the proportions of the building 


THE METAPHYSICS OF KNOWLEDGE 299 


are destroyed; new, probably ugly, proportions come into being. 
It is not simply that the spires are missing; the personality of 
the cathedral has vanished, to be replaced by another. And yet 
the two personalities have something in common; the mutilated 
whole can be pieced out to give the original; there are hints as to 
what the old personality might have been. So also in every whole 
there are suggestions of other wholes of which it might be a part. 
The presented physical object, issuing as it does from the 
unity of a mind and other physical objects not presented, must 
be a distinct “what” relative to this situation. But to call atten- 
tion to the fact that its general complexion is determined by the 
psycho-physical situation is not to deprive the presented physi- 
cal object of its reality; nor does it make the object any more 
essentially relative to mind than to the physical world beyond. 
Just as a real object other than the single notes comes into exist- 
ence when a chord in C-major is sounded, so a real (perceptual) 
physical object comes into existence in the proper situation.1 
What is the nature of the physical object when it is not per- 
ceived? All one can answer is that it cannot be exactly the same 
as when it is perceived. The situation has altered. One element, 
the element that makes the object perceptual, is absent; but just 
what aspects of the object pass out of existence with the absence 
of perception we certainly cannot say. Locke describes the un- 


1 The question of the relevance of the perceptual object to a psycho-physical 
situation is not the same as that of the “privacy” of this object for an indi- 
vidual perceiver. Every real situation is individual, and this individuality is 
determined by that of its elements; hence, there must be an individuality in 
the perceptual object which is bound up with (though not reducible to) the in- 
dividuality of the perceiving mind. But every situation has, also, its universal 
aspects, so that the “privacy” of the perceptual object is not incompatible 
with its “‘publicity.” Indeed, as has been shown in the discussion of the indi- 
vidual (above, ch. III), only the public aspects of the object are clearly and 
determinately known. The perceptions that men share are those of general 
natures and relations, 7.e., of red, motion, etc., rather than of natures and re- 
lations as individualized in particular situations, The question of the “priv- 
acy”’ of the perceptual object is one phase of the more general metaphysical 
question — how can a real object be at once individual and universal, abso- 
lutely unique yet like other real objects? See below, secs. xii and xiii. 


300 SYMBOLISM AND TRUTH 


perceived physical object as colorless, tasteless, odorless, sound- 
less, but insists that it retains its geometrical and mechanical 
properties. Yet even Locke admits that the colors, smells, tastes, 
odors, are still in the physical object as ““powers”’, that is, there 
is something in the unperceived physical situation which be- 
comes a color, taste, smell, or odor when perception is added. 
Perhaps an unperceived color differs much more widely from a 
perceived color than an unperceived motion differs from a per- 
ceived motion, but this supposition would not warrant us (fol- 
lowing the distinction between primary and secondary qualities) 
in placing some of the modes of being of the perceptual object 
only in the mind and others both in the mind and in the physical 
field beyond the mind. Certainly the whole object as unper- 
ceived is continuous with the object as perceived; the latter is a 
real whole merging with another (unperceived) real whole and 
giving indications as to its nature. 

Thus, if there is a ‘‘somewhat”’ in the perceptual object which 
is peculiar to it, there are also a vast number of properties and 
relations which are not peculiar to it, but which stretch out into 
the unperceived reality. For all reality is shot through and 
through with the general. Though each real whole is unique, it 
is still an instance of many universals which link it to other 
wholes. Physical theory seizes on certain relations and proper- 
ties found in the perceptual physical object,— for example, mo- 
tion, acceleration, mass, spatial relations, etc., — and by refin- 
ing and extending these properties and relations, so that they 
can be used as instruments of exact description, pieces out the 
picture of the whole physical reality. 


1 Along with the tendency of the mind to codperate with the elements of 
the physical situation in giving birth to the perceptual physical object goes an 
opposite tendency — the tendency not to codperate. Certain elements of the 
physical situation are excluded from the perceptual physical object. Thus, not 
only is there the problem of how the unperceived color or motion is perceived, 
but there is also the problem of why the light-waves, electrons, molecules, 
etc., are not perceived. 


THE METAPHYSICS OF KNOWLEDGE 301 


XI 


What has been said of the relation of the mind to its non- 
mental objects makes it even more difficult to believe that these 
objects are known passively by impressing themselves on the 
mind. Both the mind and a perceptual (external) object are to- 
gether in the earliest wholes of cognition. The object is in the 
mind, the mind is in the object, and there is no reason to think 
that the impulse to a more complete cognition comes — as the 
blank-sheet view of mind would have it — from the object 
rather than from the mind. It is most unlikely that the mere 
repetition of a situation in which a mind and a perceptual ob- 
ject are together leads to a clearer knowledge of the object. 
Some other factor must also be at work. The object must catch 
the attention; it must attract as well as impress the mind, and 
this means that it must complete the mind’s intention. 

Cognition is always the fulfillment of an intention, and so 
there must be native impulses to cognition from which the first 
knowledge of objects springs. The mind no less than the body 
must have its initial structure, which grows and is modified by 
successive acts of knowledge. And the structure of the mind, 
like that of the body, must be adapted to its environment. This 
is — if one wishes so to speak of it — a theory of innate ideas; 
but just as most criticisms of the “instinct psychology” object 
to the specificity of the instincts assumed rather than to the 
fact that there are instincts, so one can repudiate innate ideas 
so special as those of God, of right and wrong, of mathematical 
truth, without repudiating all innate cognitive tendencies. 

An original impulse toward analysis, toward selection or sift- 
ing, is found in knowledge. To cognize anything clearly is to 
isolate it from its surroundings. This tendency toward analysis 
is accompanied by another, the tendency to hold together with 
its surroundings what has been sifted out. Not only is a single 


302 SYMBOLISM AND TRUTH 


element more clearly known through selection, but the whole 
of which it is a part is also more clearly known. And these most 
general impulses are associated with more special ones, such as 
jumping at a noise, turning the eyes toward a light, grasping, 
etc. Indeed, every special instinct is cognitive in that it leads us 
to analyze and to take account of the unity of our environment. 
Objects do not of their own accord separate themselves out from 
experience; they might impress themselves forever on the mind 
without giving rise to the dissociation of their parts which is 
analysis. Yet reality is so put together that it permits this dis- 
memberment and also resists it, thus satisfying both the impulse 
to analysis and to unification. The mind finds real chinks and 
crannies in the object, real lines of stratification along which it 
breaks up for thought, so that we do not create out of whole 
cloth a mere appearance of analysis. We adjust ourselves 
through analysis to something real in the world beyond. (The 
reason why knowledge is for Kant an act of introversion is that 
the cognitive impulses are totally out of adjustment to reality; 
there is no trace of agreement between the way in which the 
mind tends to think and the way in which objects are beyond 
the mind. It would be strange if, with bodies so nicely adapted 
to the physical world, our mental impulses were completely 
askew to reality. The theory of evolution ought to apply to 
minds no less than to organisms.) 

Analysis is a cumulative process; what has been analyzed can 
be further analyzed, one analysis makes possible another. We 
select from what has been selected, we learn that things are to- 
gether which have not been previously observed to be together, 
the channels of cognition become more and more complex, more 
and more numerous, enabling us in the end to take account of 
subtleties, distinctions, unities, which were before obscured. 

Finally, we become aware of the widest intentions of thought, 
which make analysis possible. These are the intention to direct 


THE METAPHYSICS OF KNOWLEDGE 303 


every intention toward one and only one object (the principle of 
identity as a rule of symbolism); the intention to direct distinct 
intentions toward distinct objects (the principle of contradic- 
tion as a rule of symbolism);! and the intention to apprehend 
facts, situations, objects, as unified groups of distinct elements. 
We discover that reality yields to these intentions, that every 
object is what it is, self-identical and distinct from other ob- 
jects, yet joined with them in continuous wholes. The mind thus 
learns to be conscious of its categories, its structure, through the 
operation of these categories, the functioning of this structure, 
in concrete knowing. At the same time its contacts with special 
aspects of its environment multiply and refine its more special 
concepts. 

But the activity of the mind in the grooves of concepts would 
not bring us into touch with reality unless reality were perme- 
ated by the general. This fact is what adapts the environment to 
our cognitive impulses. Every concrete object is at once uni- 
versal and individual, absolutely unique and yet like other ob- 
jects. It is the universal — which is itself an object — which ful- 
fills our intentions in knowledge. For, as has been pointed out 
in another place,’ analysis is first of all the dissection of an 
object into a “what” and a “‘this,”’ a universal and an individual 
aspect. If there were nothing in the real which persisted, if 
every object came once and never again, our concepts could 
take hold of nothing. Reality would slip by unanalyzed, taken 
account of only in that pure awareness which lies below the level 
of clear cognition. No situation is wholly new; hence, it can be 
assimilated to knowledge held in the memory, the mind can 
come to rest in the apprehension of something which completes 
its intentions. In any moment of time (and knowledge is both 
an and of time) the mind, through the fulfillment of intentions 


1 See above, ch. VI, sec. iv. 
2 See above, ch. III, sec. i. 


304 SYMBOLISM AND TRUTH 


which bridge many times, attains a knowledge of a reality 
stretching far beyond the moment. With the conceptual tools 
forged by the aid of cruder tools, the mind digs into the object 
before it to discover principles which radiate into other objects 
— and into all reality. Thus the immediate impression is the 
occasion of true knowledge; yet knowledge in expanding beyond 
the moment does not turn upon itself to a world of appearances. 
It grows always in the direction of the real. 

In all this something which remains to be considered has 
been anticipated. It has been assumed that reality has a struc- 
ture. The essence of structure is logical form. Does reality 
exhibit logical form? Is reality made up of self-identical and 
distinct objects which coalesce into wholes (groups) with 
elements of unity and terms? Are universals, that is, elements 
of unity, real? Do the principles of identity and contradiction, 
which are the formal conditions of the being of self-identical 
and distinct objects, apply to reality? 

If these questions must be answered in the negative, not only 
does the activity of thought end in a blind-alley, but, from the 
metaphysical point of view, the truth which we have described 
as the correspondence of concepts through their structure with 
real objects becomes error. If reality is structureless, it cannot 
be adequately known through a thought bound to logical forms. 


XII 


Here is a turning-point in any metaphysics of knowledge. 
How are we to stand off from thought and hold it up beside its 
objects to discover whether the two are commensurate? If they 
are commensurate, if there can be a real identity of structure in 
concepts and the things they refer to, we cannot demonstrate 
through concepts that such an identity is possible, for this cor- 
respondence of concepts with objects is itself the condition of 
rational truth and demonstration. Nor can we know this struc- 


THE METAPHYSICS OF KNOWLEDGE 305 


tured reality in a cognitive act which takes no account of struc- 
ture. And if thought and its objects are incommensurate, we can 
not prove them to be so by going back to the negative arguments 
of agnosticism. We cannot, through the logical forms of thought, 
show that reality is without logical form; some positive knowl- 
edge, not through thought, of this formless reality would be 
needed. 

Beside agnosticism, which on purely negative grounds denies 
reason access to reality, stands positive irrationalism — a meta- 
physics which condemns reason on the strength of an intuition 
that goes deeper than thought to a mystic union with the real. 
‘Agnosticism does not successfully negate rational metaphysics. 
Does this positive irrationalism meet with better success? To 
answer this question, we must consider in what sense the act 
of cognition as a whole escapes from the concepts which at 
once confine and guide it. 

Every act of concrete knowing overflows the conceptual. To 
perceive an object is to capture in experience what one intends, 
but it is also to capture more than one intends. This is one rea- 
son why the real is alien to thought. Concepts can be multiplied 
indefinitely, yet the real object to which they lead is not ex- 
hausted and is always ready to yield further analyses, to submit 
to new descriptions. I conceive the object as a unique “some- 
what” in certain relations to other unique “somewhats’’; but 
when I grasp the object concretely I know that these concepts 
direct me only to some of its aspects. The object zs as I conceive 
it, but is also other than I conceive it; and in knowing that what 
can be picked out clearly and stated as true of the object is only 
an aspect, I must apprehend the object as transcending and in- 
cluding all its aspects. 

What has been said before of the universal and the individual 
sharpens this point. For conceptual knowledge, the individual 


306 SYMBOLISM AND TRUTH 


is always attempting to become universal by dissolving into a 
complex infinity of characters and relations, but it succeeds only 
in being an indeterminate x; while the universal is always seek- 
ing to become individual by qualifying and requalifying itself in 
an infinity of ways. If I wish to conceptualize the individuality 
of a pebble picked up on the beach, I am driven to hundreds of 
characterizations, of measurements, of minute observations; 
yet the pebble is still the x of which these relations and qualities 
can be predicated, and I cannot even be certain (with Leibniz) 
that an infinity of such predicates would distinguish this pebble. 
I cannot, in thought alone, bridge the gap between the x, which 
means indeterminately an individual, and the other concepts, 
which stand for its predicates and relations. It is in vain that I 
fill in with more predicates. In concrete knowledge the gap is 
closed, though not by concepts. I know the pebble, hold it in my 
hand, as a unique object in which all the predicates I have ob- 
served are reconciled. It is not merely that concrete knowledge 
adds sensation to thought; I do not sense the unity of the predi- 
cates in the individual. The act of knowing has pushed out be- 
yond sensation and thought to an intuition of the object. This 
intuition has been spoken of before as pure awareness. Pure 
awareness issues from thought and sensation; we cannot catch 
it in itself apart from the other phases of cognition, and yet it is 
not the same as either of these other phases. What intuition 
gives us is a residue of knowledge, left over when all that is 
clearly conceived or sensed in the object has been analyzed 
away. 

Consider the knowledge of a personality. Here intuition is 
especially prominent. Calculation, analysis, will carry one only 
a short way in adjusting himself to persons; something like 
talent, skill, tact, is needed — not a talent separated from the 
power of analysis, but a talent which makes use of every shred 
of clear knowledge, and yet does not rely wholly on clear knowl- 


KS eee ee eee ee ee eee ee 


THE METAPHYSICS OF KNOWLEDGE 307 


edge. To know a personality is to enter into that personal- 
ity, not blindly, but so that analysis plays its part and is left 
behind. 

Pure awareness is not sensation for the reason that a sensa- 
tion is atomic; it is a distinct “‘what,” e.g., this redness, this 
sourness, distinguished within a perceived whole. Moreover, a 
“pure sensation” would be a sensation of nothing whatsoever, 
for sensation cannot be thinned down till every vestige of mean- 
ing, thought, has been wiped away. When this search for a 
“pure sensation”’ is pursued, the sensum approaches a vanish- 
ing point. A “‘pure sensation” is the thinnest of abstractions, an 
_ imaginary limit which cognition never reaches. When knowledge 
overflows the conceptual, it does not do so in the direction of 
sensation. Nor does knowledge pass beyond concepts by going 
to the other extreme, by sifting out all traces of sensation, leav- 
ing the materials of experience behind and attaining an esoteric 
vision of a reality that never was and never could be found in 
perception. Yet to speak of pure awareness, of non-conceptual 
knowledge, is to suggest the one or the other of these views — 
sensationalism, or rationalism become esoteric. 

An act of concrete knowing is bathed in an atmosphere of the 
non-conceptual; it has a part of its being in a medium which is 
neither pure thought nor pure sensation; and no act of concrete 
knowing is complete until it finds itself surrounded and upheld 
by the non-conceptual. This ever-present background of pure 
awareness tends, like other backgrounds, to be forgotten and to 
emerge only when a foreground has been clearly distinguished. 
But it is always there, bringing thought and sensation together 
and completing knowledge as neither thought nor sensation can. 
It is impossible to isolate thought from sensation, and equally 
impossible to isolate pure awareness from sensation and thought. 
Perceptual thought transforms itself into pure awareness and 
pure awareness passes smoothly into perceptual thought. There 


308 SYMBOLISM AND TRUTH 


is no pure awareness dissociated from these other modes of cog- 
nition. 

An anti-intellectualistic philosophy such as M. Bergson’s 
wishes to set pure awareness or intuition on its own feet, to 
sever rational thought from the non-conceptual medium into 
which and from which it flows. M. Bergson does violence to the 
cognitive act; he looks at cognition abstractly in the very effort 
to fasten on that which is most concrete in it. Instead of seeing 
it as it is, a fusion of reason, sensation, and intuition, he exalts 
the irrational component at the expense of the rational. 

“By intuition,” M. Bergson explains, “is meant the kind of 
intellectual sympathy by which one places oneself within an ob- 
ject in order to coincide with what is unique in it and conse- 
quently inexpressible. Analysis, on the contrary, is the opera- 
tion which reduces the object to elements already known, that 
is, to elements common both to itself and to other objects. To 
analyze, therefore, is to express a thing as a function of some- 
thing other than itself. All analysis is thus a translation, a de- 
velopment into symbols, a representation taken from successive 
points of view from which we note as many resemblances as 
possible between the new object which we are studying and 
others which we believe we know already. In its eternally un- 
satisfied desire to embrace the object around which it is com- 
pelled to turn, analysis multiplies without end the number of its 
points of view in order to complete its always incomplete repre- 
snetation, and ceaselessly varies its symbols that it may perfect 
the always imperfect translation. It goes on, therefore, to infin- 
ity. But intuition is a simple act.” ! 

M. Bergson’s writings, like his snowball rolling down hill and 
growing as it rolls, bulk together to force it on the mind that 
concrete knowing is more than analysis. But that analysis is es- 


1 H. Bergson, An Introduction to Metaphysics, T. E. Hulme’s translation 
(1912), p. 8. 


THE METAPHYSICS OF KNOWLEDGE 309 


sentially falsification, that intuition enters into reality to find a 
changing, formless, flowing durée which eludes all concepts — 
these are conclusions which follow only from making a part of 
concrete knowing equal to the whole. M. Bergson is Heracleitus 
with the logos left out. If reality is change, this fact, as Heraclei- 
tus observed, does not itself change, and here is an entering 
wedge for the permanent. An intuition cut off from concepts 
could not name the reality it knows. Just as the concrete con- 
tent of pure sensation or of pure thought would approach a zero, 
so the concrete content of pure intuition tends to be nothing. 
M. Bergson insists, for example, that to conceive a motion as an 
infinite series of brief motions taking place at point-instants ar- 
ranged in order is to fail to know the passage which is the es- 
sence of the motion. One must identify himself with this passage 
by intuition. Yet this pure intuition of the wholeness of the mo- 
tion is, in itself, no less empty than the representation in terms 
of point-instants. Though there is something real in the passage 
which is given only in intuition, there is also something real in it 
which corresponds to the conceptual series of point-instants.’ 
To know the motion either simply as passage or simply as a re- 
lated series of motions at point-instants is, in each case, to have 
an insecure hold on its reality. 

Irrationalism springs from a desire deeply rooted in human 
nature — the desire to give oneself up, like a resting swimmer 
on a bright sea, to the sustaining buoyancy of a limitless and 
intimate reality. But one knows the buoyancy of the sea only 
by learning to swim, and one knows reality only by learning to 
think out his intuitions and to gain new intuitions through his 
thought. 

M. Bergson’s feeling that the deliverances of intuition prove 


1 See A. N. Whitehead, The Principles of Natural Knowledge (1919), chs. 8, 
9, 10, 11 on extensive abstraction for a definition of points and instants which 
correlates these entities with the perceived reality. 


310 SYMBOLISM AND TRUTH 


the inadequacy of thought cannot rest on a contradiction be- 
tween what is known without concepts and what is known in 
concepts, for contradiction has meaning only where concepts 
apply. Intuition could not contradict reason. When the cogni- 
tive act is taken in its wholeness as the convergence of thought, 
sensation, and intuition upon an object, this feeling of the inad- 
equacy of thought to reality melts away. Though one is aware 
that reality is not completely compressed into the molds of 
reason, he still finds something in the real which fits these 
molds. Reality exhibits logical form. 


XI 


That reality is logical in form means that the distinction be- 
tween terms and the universals, that is, the qualities and rela- 
tions, which modify and unite these terms, is a real distinction. 
It means that there are basic terms, individuals, about which 
qualities and relations cluster to form concrete facts. It means 
that every object, whether individual or universal, is self-identi- 
cal and distinct from other objects, and finally that these ob- 
jects unite into wholes, groups, which are themselves real ob- 
jects. 

For Kant it is just this logical form which is created by 
thought and which confines thought to a world of phenomena; 
and for M. Bergson this logical form is the product of a platoniz- 
ing intellect. But since the mind from the outset of knowledge 
is in contact with the real, in knowing objects it must be able 
to know that logical form is in reality and not merely in a mind 
compelled to think in this fashion. This is the first and most 
fundamental metaphysical insight. 

Let us return to the vis sua nativa of the intellect of which 
Spinoza speaks. If there is any knowledge, there is a metaphysi- 
cal insight which upholds knowledge at every stage and which 
becomes conscious of its own general intentions and, through 





>? a oe 


THE METAPHYSICS OF KNOWLEDGE 311 


these, of the general structure of reality, when knowledge is faced 
with the question of its own validity. To know is, from the be- 
ginning, to have an insight into the real. This power is not at- 
tained after long meditation. It is not by falling into antinomies 
and seeking a way out that thought is enabled finally to seize 
reality; nor is it by dismembering the act of knowledge and at- 
tempting to know through pure sensation, pure reason, or pure 
intuition. This power is a crude and original endowment of the 
mind. It is manifest in the simplest act of concrete knowing, not 
as one component but as the very life of the act itself. To reflect 
on knowledge, to ask how we can know and what we can know, 
is to bring this original metaphysical insight to a consciousness 
of itself. Instead of being aware of objects as fulfilling specific 
intentions, as being of this or that sort, we become aware of ob- 
jects as fulfilling the most general intentions of thought, and 
thus we discover the logical structure of the reality to which our 
thought is from the first adapted, and from which it is never cut 
off. We cannot step outside the act of knowledge to an intuition 
which renders all knowledge but itself invalid. 

Knowledge from its inception embraces a reality which is 
logical in form, without being aware of what constitutes logical 
form. We do not pause to reflect that in knowing we are distin- 
guishing terms from their qualities and relations, that we are 
taking some terms as individual, that we are treating objects as 
self-identical and distinct, though as united into real wholes. 
But if we do pause to reflect, we know that only because objects 
conform to these highly general conditions are they real. To 
know that the widest intentions of thought are fulfilled by ob- 
jects is to tighten rather than loosen the native grasp of the 
mind on reality. In perceiving the logical framework of the real- 
ity within which it operates, the mind knows its own power with 
a new clarity. 

That concrete knowing even of the most elementary sort is 


312 SYMBOLISM AND TRUTH 


insight into the real, and that the act of knowing as a whole is 
the source of this insight, are the basic propositions of a meta- 
physics which justifies knowledge. These propositions do not 
assert that all concrete knowledge is true. An object may not be 
as it is known, it may be misconceived. But even a miscon- 
ceived object zs, if it is known concretely; it is there to be reck- 
oned with, to be fitted into the scheme of reality. The act of 
knowledge, becoming conscious of itself, reveals the essential pat- 
tern of this scheme, but it does not reach through more readily 
to the details than it would without this self-consciousness. By 
discovering that the general principles of knowledge are rooted 
in the general structure of the real, we learn that a rational 
truth is possible, but we do not establish specific truths. Spe- 
cific truths must be hewn out laboriously from the materials of 
experience by many cumulating acts of knowing. The details 
must be fitted into the general pattern, and for this the skill 
which grows with the expansion of knowledge is needed. 

Thus in one direction knowledge is complete, it can take se- 
cure hold of the form of the real; while in another direction it is 
never complete, it is being continually enlarged and fortified by 
new details. 

Within the essential scheme of the real, there is room for an 
infinite variety of detail. The form is in the detail; the variety of 
detail, in the form. The metaphysical insight which makes use 
of the complete cognitive act shows us how passing and tem- 
porary objects embody universal principles and yet are them- 
selves unique products of an ever-renewed process of becoming. 
Reality is as changeful and growing as M. Bergson finds it to be, 
but the change is an affirmation rather than a denial of logical 
form. Against the newness, the individuality, of the thing of the 
moment, the universal, which is neither new nor individual, 
stands out. M. Bergson condemns analysis because it must “ex- 
press a thing as a function of something other than itself” and 


THE METAPHYSICS OF KNOWLEDGE 313 


so miss what is unique in the thing. One can condemn pure in- 
tuition because, in refusing to express a thing as a function of 
something other than itself, it misses what is not unique in the 
thing — and so fails to know this very uniqueness as sharply as 
might be if analysis were joined to intuition. 

To the irrationalist, reality cannot be self-contradictory for 
this reason, that it resists concepts — and contradiction is a logi- 
cal relation between concepts; the term has no meaning for him 
as applied to the real. The reality known through the fuller 
metaphysical insight of which we are speaking is non-contra- 
dictory in another sense; the principles of identity and contra- 
diction can be truly affirmed of it. This reality can be consist- 
ently presented and represented through concepts. And yet, if 
we consider these principles themselves, it is plain that they 
permit an endless mutability of the particular. As statements 
about the real world they affirm that “any object is identical 
with itself and distinct from other objects,” but they give us no 
information as to what objects are self-identical and distinct. 
They tell us merely that, however tangled the lines of identity 
and distinctness may be, there must still be such lines. Con- 
sistency has thus its metaphysical basis as a test of truth which 
is valid even though no experience includes a reality which is 
complete, full-grown, in every respect. Judgments can go on 
correcting themselves by their consistency even though con- 
sistency does not determine the subject-matter of any truth. 

This infinite perfectibility of knowledge does not lead to the 
corollary that there is no truth except through an infinite pro- 
cess of correction. We know the logical form of reality without 
such a process; logical form is a perfectly general aspect of the 
real which can be grasped in finite knowledge. Yet it is only an 
aspect. And if we can know one perfectly general aspect of real- 
ity in finite knowledge, we can know others— provided there are 


such aspects to be known. 


314 SYMBOLISM AND TRUTH 


The laws of nature seem to hang midway between these 
purely formal principles and particular truths. It is possible, as 
C. S. Peirce, H. Poincare,’ and others have suggested, that 
whole systems of natural law are superseded by other systems, 
as one event in history is superseded by another, or old sets of 
personal habits by new ones. But if the universe, from time to 
time, gives up one general mode of behavior to adopt another, it 
does not contradict itself. The particular events of history can 
be truly known, so long as we do not insist that they are more 
than particular events; and so a system of natural laws, which 
might dissolve and pass, could be truly known if we did not be- 
lieve it to be eternal — if we could see what went before and 
came after. But just as every set of personal habits embodies the 
laws of human psychology, so every one of a successive infinity 
of cosmic habits would embody the psychology of the universe. 
And even if the laws of this cosmic psychology were more con- 
crete than the formal principles of structure we have discussed, 
they could be known in perfect generality. 

Whatever the whole of reality may be — if there be a whole— 
we can be certain that we do not know this whole. A complete 
understanding of any whole rests on a knowledge of its parts, 
and a complete understanding of the parts on a knowledge of 
the whole, but it does not follow that there are no truths which 
are valid for the parts alone. Though the process of the growth, 
the becoming, of reality may go on infinitely, and though it may 
be impossible to know all there is (or will be) to be known con- 
cerning any fragment of the real — unless it be in a mind which 
spans this infinite process,— still these considerations do not 
demonstrate the impossibility of attaining truth in a knowledge 
which is immersed in the process of becoming. 


1 C.S. Peirce, Chance, Love, and Logic (1923), ““The Doctrine of Necessity 
Examined”; also, H. Poincare, La Valeur de la Science (1905), ch. 11, and 
Derniéres Pensées (1913), ch. 1. 


THE METAPHYSICS OF KNOWLEDGE 315 


XIV 


No criticism of knowledge, then, can destroy knowledge; no 

theory of appearances can prove that reality is unknown or un- 
knowable. For a knowledge of even the most contradictory of 
appearances is the beginning of an insight into the real. The 
theory of knowledge clarifies this insight as one clarifies his 
speech by learning the grammar of the language to which he is 
born. But without speech we could not learn the rules of speech, 
and without true knowledge we could not construct a theory of 
truth. 
_ At the poles of knowledge, beyond clear statement and ra- 
tional proof or disproof, are scepticism and mysticism. The 
sceptic believes nothing he can state; the mystic can state 
nothing he believes. Rational knowledge shares with scepticism 
a readiness to revise itself but refuses to join scepticism in re- 
vising itself into a state of total incredulity. Something stands 
firm, if it be no more than the good sense which Descartes found 
“is of all things among men the most equally distributed.” With 
the irrationalist and the mystic, rational knowledge shares the 
conviction that reality cannot be completely packed into neat 
concepts, but rational knowledge cannot believe that there is no 
neatness in reality, that because something escapes nice formu- 
lation, everything does. 

Making use of all the instruments at its command — sensa- 
tion, thought, intuition — knowledge can reflect on its own pro- 
cesses and reaffirm, as against scepticism, mysticism, and ag- 
nosticism, its own ability to take at least partial possession of 
the real in a rational experience. But in order to know, it is not 
necessary to inquire how it is possible to know. As the lungs are 
prepared by nature for breathing, the hands for grasping, the 
legs for walking, so the mind is prepared for knowing. We may 
with infinite patience lay bare the anatomy of the mind, but we 


316 SYMBOLISM AND TRUTH 


cannot in doing so discover that the mind’s function is to trick — 
us or to shut us off from the real. The air the mind breathes, the 
substance it grasps, the ground it walks on, is reality. The theory 
of knowledge, like the knife of the surgeon, may be able to sepa- 
rate the delicately woven tissues of thought, but it cannot give 
or take away the power to know. 





SUPPLEMENTARY READINGS 


Tars list of supplementary readings is not a bibliography; it is in- 
tended to bring together for the use of the student some of the contem- 
porary literature — chiefly in English — on the theory of knowledge, 
and to suggest directions in which the topics treated in the text can 
be expanded. It will be well for the reader to take up the selections 
under each heading in the order given here; the readings most closely 
allied to the text are placed first in each group. References to the 
classical philosophers are omitted, except in a few instances. 


INTRODUCTION 


On the relation of the theory of knowledge to metaphysics: 
C. D. Broad, Scientific Thought (1923), Introduction. 
W. T. Marvin, The New Realism (1912), “The Emancipation of 
Metaphysics from Epistemology.” 
S. Alexander, Space, Time, and Deity (1920), Introduction. 


Cuapter I, Meaninea 


On the psychology of meaning: 

E. B. Titchener, The Experimental Psychology of the Thought Process 
(1909), Lect. 2, “‘Reference to Object as the Criterion of Mind,” 
Lect. 5, “The Experimental Psychology of the Thought Process.” 

E. Rignano, The Psychology of Reasoning (1923), ch. 4, “What is 
Reasoning?” 

K. Koffka, The Growth of Mind (1924), ch. 5, sec. 10, “The First Use 
of Language.” 

J. B. Watson, Psychology from the Standpoint of a Behaviorist (1919) 
ch. 9, secs. A, B, “Explicit and Implicit Language Habits.” 

G. F. Stout, Analytic Psychology (1896), bk. ii, ch. 10, “Thought 
and Language.” 

On the philosophy of meaning: 

F. C. S. Schiller, B. Russell, H. H. Joachim, Mind, N. S. vol. 29 
(1920), pp. 385 ff., “The Meaning of Meaning, a Symposium.” 

R. F. A. Hoernlé, Mind, N. S. vol. 16 (1907), pp. 70 ff., “Image, 
Idea, and Meaning.” 

C. K. Ogden and I. A. Richards, The Meaning of Meaning (1923), 
ch. 2, part 2, “Towards a Science of Symbolism,” ch. 9, “The 
Meaning of Meaning,” ch. 10, “Symbol Situations.” 

On mediate and immediate knowledge: 

W. James, The Principles of Psychology (1890), vol. 1, ch. 8, “The 
Relations of Minds to Other Things,” ch. 9, “The Stream of 
Thought.” 

317 


318 SUPPLEMENTARY READINGS 


G. F. Stout, Analytic Psychology (1896), bk. i, ch. 2, ““The Analysis 
of Presentations,” ch. 3, “The Apprehension of Form,” bk. ii, 
ch. 5, ““Noetic Synthesis.” 

J. Ward, Psychological Principles (1918), ch. 4, secs. 1, 2, “‘The 
Presentational Continuum,” ch. 6, secs. 1, 2, 6, 7, “‘Perception,” 
ch. 12, “Thought and Language.” 


Cuapter II, Logica Form 


On the structure of complexes: 
B. Russell, Monist, vol. 28 (1918), pp. 509 ff., “The Philosophy of 
Logical Atomism,” lect. 2. 
L. Wittgenstein, Tractatus Logico-Philosophicus (1922), Introduction 
(by B. Russell), Preface, and Text through prop. 4.04. 


On identity and diversity: 
G. E. Moore, Proceedings of the Aristotelian Society, vol. 1 (1900- 
1901), pp. 103 ff., “Identity.” 


Cuapter III, Universats AND INDIVIDUALS: ORDER 


On universals and individuals: 

J. Laird, A Study in Realism (1920), ch. 6, “‘ Principles.” 

S. Alexander, Space, Time, and Deity (1920), vol. 1, bk. i, ch. 3, 
“Universal, Particular, Individual,” ch. 4, “‘ Relation.” 

B. Russell, Proceedings of the Aristotelian Society, vol. 12 (1911-1912), 
pp. 1 ff., “On the Relations of Universals and Particulars.” 

G. F. Stout, Proceedings of the British Academy (1921), “The Nature 
of Universals and Propositions.” 

W. E. Johnson, Logic (1921), Part I, ch. 11, ‘“‘The Determinable,” 
ch. 12, ““The Relation of Identity,” ch. 13, “Relations or Transi- 
tive Adjectives.” 


On space, time, and objects: 

C. D. Broad, Scientific Thought (1923), ch. 1, ‘The Traditional Con- 
ception of Space and the Principle of Extensive Abstraction,” 
ch. 2, “Time and Change.” 

A. N. Whitehead, The Concept of Nature (1920), ch. 3, “Time,” ch. 5, 
“Space and Motion,” ch. 7, “Objects”; also, The Principles of 
Natural Knowledge (1919), Part II, ch. 6, “Events,” ch. .7, 
“Objects.” 


On abstraction: 
G. Berkeley, The Principles of Human Knowledge (1710), Introduc- 
tion. 
A. N. Whitehead, The Principles of Natural Knowledge (1919), 
Part II, chs. 8, 9, ‘Extensive Abstraction.” 


On order: 
B. Russell, The Principles of Mathematics (1903), ch. 9, “Relations.” 
S. Alexander, Space, Time, and Deity (1920), vol. i, bk. i, ch. 5, 
“Order.” 


SS) eS a eel 


SUPPLEMENTARY READINGS 319 


CuHapteR IV, Description AND ANALYSIS 


On naming, description, and the variable: 

B. Russell, The Problems of Philosophy, ch. 5, ‘Knowledge by Ac- 
quaintance and Knowledge by Description,” ch. 9, “The World 
of Universals”; also, The Principles of Mathematics (1903), 
ch. 5, “On Denoting,” ch. 8, “The Variable’; and Mind, N. S., 
vol. 15 (1905), pp. 479 ff., “On Denoting.” 

B. Bosanquet, Logic (1888), vol. 1, Introduction. 

A. N. Whitehead, An Introduction to Mathematics (1911), ch. 2, 
“Variables,” ch. 5, “The Symbolism of Mathematics.” 


On internal and external relations: 
F. H. Bradley, Appearance and Reality (1893), ch. 2, “Substantive 
and Adjective,” ch. 3, “Relation and Quality.” 
G. E. Moore, Philosophical Studies (1922), ch. 9, ‘‘External and In- 
ternal Relations.” 


Cuapter V, TrutH anv Fatsity 


On truth and falsity: 

L. A. Reid, Knowledge and Truth (1923), omitting ch. 9 (for a gen- 
eral survey of contemporary theories of truth). 

S. Alexander, Space, Time, and Deity (1920), vol. 2, bk. iti, ch. 8, 
“Tllusion and Ideas,” ch. 9, sec. B, “Truth and Error.” 

F. H. Bradley, Essays on Truth and Reality (1914), ch. 5, “On Truth 
and Copying,” ch. 9, “On Appearance, Error, and Contradic- 
tion.” 

H. H. Joachim, The Nature of Truth (1906), ch. 1, ““Truth as Corre- 
spondence,”’ ch. 3, Part I, ‘““The Coherence Notion of Truth.” 


On sensation and perception: 

Plato, Theaetetus, Jowett’s translation. 

J. Laird, A Study in Realism (1920), ch. 2, “The Things We Per- 
ceive.” 

R. F. A. Hoernlé, Studies in Contemporary Metaphysics (1920), 
ch. 4, “On ‘Doubting the Reality of the World of Sense’,”’ ch. 5, 
***Saving the Appearances’ in the Physical World.” 

W. James, The Principles of Psychology (1890), vol. 2, ch. 21, ‘The 
Perception of Reality.” 

B. Russell, Our Knowledge of the External World (1914), Lect. 3, 
‘The External World.” 

C. D. Broad, Scientific Thought (1923), ch. 7, “‘Matter and its Ap- 
pearances,”’ ch. 8, ““The Theory of Sensa.” 


On the theory of “objectives”: 
G. D. Hicks, Mind, N.5S., vol. 31 (1922), pp. 1 ff., “‘The Philosophical 
Researches of Meinong.”’ 
B. Russell, Mind, N. §., vol. 13 (1904), pp. 204 ff., 336 ff., 509 ff., 
*Meinong’s Theory of Complexes and Assumptions.” 





320 SUPPLEMENTARY READINGS 


On belief: 
D. Hume, A Treatise of Human Nature (1738), bk. i, Part ITI, secs. 7, 
8, 10. 
F. C.S. Schiller, Problems of Belief (1924), chs. 1, 3, 9, 10, 11, 12. 
C. S. Peirce, Chance, Love, and Logic (1923), First Paper, “The 
Fixation of Belief.” 


CuapterR VI, NEGATION AND CONTRADICTION 


Se . 


On negation: 
R. Demos, Mind, N. S., vol. 24 (1917), pp. 188 ff., “A Discussion of 
a Certain Type of Negative Proposition.” 
F. H. Bradley, The Principles of Logic (2d ed. 1922), vol. 1, bk. i, 
ch. 3, “The Negative Judgment,” and Terminal Essay 6. 
B. Bosanquet, Logic (1888), vol. 1, ch. 7, secs. 1, 2, 3, 5. 
W. E. Johnson, Logic (1921), Part I, ch. 5, “Negation.” 
H. Bergson, Creative Evolution (1911, transl. by A. Mitchell), ch. 4, 
“The Idea of Nothing.” 
On contradiction and the “‘laws of thought”: 
F. C.S. Schiller, Formal Logic (1912), ch. 10, “The Laws of Thought.” 
C. Sigwart, Logic (2d ed. 1895, transl.), vol. 1, ch. 4, “The Negation.” 


ee a ee ee ee ee 


Cuapter VII, Format DepuctTIion 


On formal deduction in general: 

J. W. Young, Fundamental Concepts of Algebra and Geometry (1911), 
lects. 1, 4, 5, 19, 21. 

A. N. Whitehead, A Treatise on Universal Algebra (1898), ch. 1, 
“On the Nature of a Calculus.” 

C. I. Lewis, A Survey of Symbolic Logic (1918), ch. 6, secs. 1, 3. 

L. Couturat, La Logique de Leibniz (Paris, 1901), ch. 4, sec. 4 ff., 
“La Caractéristique Universelle.”’ 

On the Boolean Algebra: 

E. V. Huntington, Transactions of the American Mathematical So- 
ciety, vol. 5, no. 3 (1904), pp. 288 ff., “Sets of Independent Pos- 
tulates for the Algebra of Logic.” 

H. M. Sheffer, Transactions of the American Mathematical Society, 
vol. 14, no. 4 (1913), pp. 481 ff., “A Set of Five Independent 
Postulates for Boolean Algebra.” 


> 


sis 


CuHapter VIII, Toe Merapnysics or KNowLEDGE 


On appearance and reality: 

F. H. Bradley, Appearance and Reality (1893), bk. xi, chs. 13, 14, 
“The General Nature of Reality,” ch. 15, “‘Thought and Real- 
ity,” ch. 27, “Ultimate Doubts.” 

J. Ward, Naturalism and Agnosticism (1899), vol. i, Introduction, 
vol. 2, Part IV, lects. 14, 15. 

A. J. Balfour, A Defence of Philosophic Doubt (1879), ch. 1, “On the 
Idea of a Philosophy,” ch. 6, “Transcendentalism,” ch. 13, 
“Evolution of Belief.’ 


Sg ee SR ee ee a ee a ee 





Se 


SUPPLEMENTARY READINGS 321 


On the relation of mind and its objects: 
W. James, Essays in Radical Empiricism (1912), Essay 1, ‘Does 
Consciousness Exist?” 
S. Alexander, Space, Time, and Deity (1920), vol. 2, bk. iii, ch. 4, 
“Mind and Knowing.” 
R. B. Perry, Present Philosophical Tendencies (1912), Part V, ch. 13, 
““A Realistic Theory of Knowledge.” 


On idealism and its critics: 

R. F. A. Hoernlé, Idealism (1924), especially chs. 4, 5, “Idealism as 
the Theory of the Absolute.” 

J. Royce, The World and the Individual (1900), vol. 1, lects. 3, 4, 5, 
6, 7, 8, 10 (an examination of realism, mysticism, Kantianism, 
and absolute idealism). 

T. H. Greene, Prolegomena to Ethics (1883), bk. i, ch. 1, “The Spirit- 
ual Principle in Knowledge and in Nature,” ch. 2, “The Relation 
of Man as Intelligence to the Spiritual Principle in Nature.” 

R. B. Perry, Present Philosophical Tendencies (1912), Part III, ch. 6, 
“The Cardinal Principle of Idealism,” ch. 7, “Objective or 
Transcendental Idealism.” 

On intuitionism: 

H. Bergson, Creative Evolution (1911, transl. by A. Mitchell), In- 
troduction, ch. 4, pp. 298 ff., “‘Form and Becoming’’; also An 
Introduction to Metaphysics (1912, trans. by E. Hulme). 


General reference: 
C. D. Macintosh, The Problem of Knowledge (1915). 











INDEX 


“A,”? 120, 121, 145. 

Absolute, The, 175, 277, 285. 

Absolute Idealism, 272, 273. 

Abstract facts, 82, 106. 

Abstract ideas, 85. 

Abstract thought, 117. 

Abstraction, 83-85, 88, 106. 

Absurdity, 94, 95. 

Acquaintance, 13, 38. 

Action, versus thought, 28. 

Active form, grammatical, 98. 

Adjectives, 89 ff., 117. 

Agnosticism, 268 ff., 278, 279. 

Algebra, Boolean, 335 ff. 

“All,” 140. 

Ambiguity, 56; logical, 119 ff.; psy- 
chological, 119, 120; of the nega- 
tive, 198 ff., 219. 

Ambiguous truth and falsity, 212 ff. 

An,” 120, 121. 

Analysis, 31, 47,54, 64, ch. iv (108 ff.), 
126; original impulse to, 301, 302. 

Analytic form, in scientific knowl- 
edge, 133 ff. 

Analytic judgments, 126 ff., 131, 147. 

Analytical representation, 31. 

Antinomies, Kantian, 169, 277. 

Antirationalism, 169, 305 ff. 

“Any,” 121, 122, 145. 

Appearance, 150; and reality, 272 ff., 
280. 

A priori, The, 208, 219. 

Aristotle, 44, 66, 84, 132, 173, 188, 
267, 282 (note), 287. 

Assertion, of descriptions, 145, 146. 

Assertion, 179 ff., 184, 185; sign of, 
185. 

Association, 22. 

Asymmetry, 96 ff. 

Aufgabe, 17, 22. 

Awareness, pure, 18, 20, 39, 43, 66, 
157, 305 ff. 


Bacon, F., 5, 7. 

Behaviorism, theory of meaning, 
25 ff. 

Belief, 16, 24, 25, 29, 37, 149, 179 ff., 
195; and inference 255 ff. 

Bergson, H., 18, 89, 169, 289, 312, 
313; theory of intuition, 308 ff. 

Berkeley, 7, 21, 85, 162, 274, 284, 285, 
288. 

Boolean Algebra, 235 ff. 

Bradley, F. H., 67, 89, 277. 

Broad, C. D., 8. 


Carroll, Lewis, 94, 118. 

Case, grammatical distinctions of, 98. 

Categories, 194; Kantian, 171; em- 
pirical, 171; principles of identity 
and contradiction as formal cate- 
gories, 208. 

Change, 69 ff., 77, 78, 105. 

Classes, 140 ff.; infinite, 143; of one 
member, 143; logic of, 243 ff. 

Coherence theory of truth, 175 ff, 
194. 

Commutative law, 100, 247. 

Comparison, 87. 

Completely inferential systems, 259, 
264. 

Complexes, 30, 42 ff.; order of poly- 
adic complexes, 98; meaning of, 
154, 155. 

Complex elements of unity, 103 ff., 
107. 

Complex objects, 35. 

Complex symbols, 35 ff. 

Conception, 17, 38. 

Conceptual validity, distinguished 
from truth, 218, 219. 

Concrete facts, 82, 106. 

Concrete thought, 282, 283. 

Condensation of substitutions, 234. 

Connoting, 111. 


325 


326 


Consistency, 168 ff., 194; as truth, 
174; formal, 218, 223; as a real 
category, 313. 

Constants, functional, 252. 

Construction of concepts, 156; con- 
structs, 165. 

Continuity, of mind and objects, 276, 
293-295. 

Contradiction, principle of, ch. vi 
(205 ff.), 219, 226; as a formal 
category, 208. 

Copula, 185. 

Correspondence, 42; of form, 52; of 
symbols and objects, 60. 

Correspondence theory of truth, 
173 ff., 176 ff., 192. 

Critical philosophy, 270 ff. 


Data, 34; sense data, 14ff., 19, 
160 ff.; reality of, 159 ff., 193. 

Deduction, ch. vii (222 ff.), 261 ff. 

Deductive systems, 92; conditions of 
significance and truth in, 258 ff. 

Definition, 32, 34, 58, 118, 146, 226, 
236, 231%. 

Demos, R., theory of negation, 198 ff., 
219. 

Denial, 185 ff.; bare, 215; privation 
of ground, 216; positive denial, 
216 ff. 

Denoting, 109 ff. 

Descartes, 70, 287, 315. 

Description, 35, 74, ch. iv (108 ff.); 
of universals, 122; form of, 112, 
113, 145; assertion of, 145, 146. 

Determinism, 68, 72. 

‘Determination is negation,”’ 205. 

Dialectic, Kantian, 277, 278. 

Disbelief, 185 ff., 196, 215. 

Distinctness of meaning, as basis of 
negation, 203 ff. 

Diversity, numerical, 46, 59, 60; per- 
ception of, 68; as a real category, 
313 

Dreams, 162 ff. 

Dualism, epistemological, 274; Car- 
tesian, 287, 288. 


“*Each,” 143. 
Empiricism, 165 ff. 


INDEX 


Equations of structure, 233, 236. 

Equivalence, 58. 

Equivocation, 56, 57, 64, 119. 

Error, 16, 149, 163 ff., 172, 173, 191. 

Essence, 66. 

Euclidean space, 134 ff., 147. 

“Every,” 143. 

Excluded middle, 186, 208 ff., 219. 

Existence, criteria of, 159 ff.; as a 
predicate, 183; limited meaning of, 
193. 

External relations, 130. 


Fact, 44 ff., 65; unity of, 78 ff.; con- 
crete, 82; abstract, 82; syntax of, 
91; negative, 197 ff., 219. 

Falsity, 148, ch. v (149 ff.), 193, 197; 
ambiguous falsity, 212 ff. 

Fancy, 188. 

First philosophy, 195. 

Form, 37; of objects, 43; logical 
form, ch. ii (41 ff.), 78 ff.; general 
schematism of, 52; correspondence 
of, 53; presentation of, 107; of 
descriptions, 112, 113, 145; objec- 
tivity of symbolic form, 156; iden- 
tity of form in fact and symbol, 
178; science of pure form, 222. 

Function, 45. 

Functional constants, 252. 

Functional range, 249 ff. 

Functional variability, 249 ff., 263. 


Generalization, 116 ff. 

Geometry, 134 ff.; Euclidean, 147, 
222; non-Euclidean, 134f., 147,222. 

Grammar, 37, 40; of symbolism,. 
89 ff., 106. 

Ground, of negation, 200, 204, 216 ff.; 
privation of, 216. 

Groups, symbolic, 35 ff., 40; defini- 
tion of a group, 45 ff., 64; type of, 
47, 48, 63; multiplicity of, 48, 63; 
major members of, 48, 49; reflex- 
ive, 61, 62; unity of, 78 ff. 

Group meaning, 31 ff. 


Habits, of meaning, 26; of language, 
27. 
Heracleitus, 309. 





INDEX 


Hobbes, 22, 149, 179, 260. 

Holt, E. B., 287 (note). 

Hume, 7, 8, 59, 60, 162; theory of 
belief, 180 ff.; scepticism, 189 ff.; 
276, 291, 292. 

Huntington, E. V., 228, 232, 233, 243. 

Husserl, E., 8. 


Idealism, 272, 273, 284 ff., 289. 

Ideas, 9 ff., 38; abstract, 85; innate, 
301. 

Identity, 44, 46; statements of, 54; 
principle of, 56-58, 64, 139, 206, 
207, 226; of objects, 56, 59; of 
indiscernibles, 71, 74; of univer- 
sals, 76 ff.; of the variable, 118; of 
meaning, 126 ff.; as a formal cate- 
gory, 208; as a real category, 313. 

Tllusion, 163, 164. 

Images, 10 ff., 38, 94, 95, 153, 292. 

Imagination, 35, 36, 73; syntax of, 
93 ff.; constructive, 181; and rea- 
son, 260, 261. 

Immediate knowledge, 13 ff., 19, 38, 
305 ff. 

Implications, in formal systems, 233, 
234, 251, 252. 

Incompatibility, 200, 219. 

Incomplete symbols, 108 ff., 124. 

Incompletely inferential systems, 259, 
260, 264. 

Incredulity, 187 ff. 

Indiscernibles, identity of, '71, 74. 

Individuality, reality of, 306. 

Individuals, ch. iii (66 ff.); determi- 
nation of, by universals, 67 ff.; 
principle of individuation, 70; 
representation of, 71, 72; bare in- 
dividuals, 129. 

Induction, 168. 

Anference, 223; general nature of, 
255 ff., 263. 

Inferential negation, 211. 

Infinite classes, 143. 

Infinite negative, 217. 

Innate ideas, 301. 

Insight, metaphysical, 272, 277, 279, 

. 810 fi. 

Intention, 29, 38, 39. 

Internal relations, 130. 


327 


Interpretation, signs of, 120ff.; of 
formal systems, 224 ff., 242 ff. 

Intuition, 18 ff., 20, 43, 165, 279, 301, 
305 fi. 

Irrationalism, 305 ff. 

V8 7185. 


James, W., 15, 16, 22, 24, 165, 186; 
theory of consciousness, 291. 

Joachim, H. H., 175 ff. 

Judgment, 179 ff.; synthetic, 126 ff.; 
analytic, 126 ff.; inference as a 
form of, 257. 


Kant, 7, 81, 88, 131, 158, 167, 168, 
169, 171, 182, 190, 208; agnosti- 
cism, 270 ff., 290, 302, 310. 

Knowing relation, 295, 296. 

Kiilpe, O., 17 (note). 


Language, 51, 81, 90; habits of, 27; 
origin of, 33; syntax of, 93 ff., 102; 
inference in, 259, 260. 

Laws, 89, 147; of thought, 205 ff. 

Leibniz, 71, 72, 74, 105; theory of 
truth and deduction, 264, 265 
(note), 306. 

Locke, 7, 9, 10, 22, 30, 85, 127, 167, 
176; agnosticism, 270ff., 293, 
299, 300. 

Logic, 5; formal logic, 201, 202, 222; 
algebra of, 235 ff.; of classes, 
248 ff. 

Logical ambiguity, 119 ff. 

Logical form, ch. ii (41 ff.); general 
schematism of, 52; reality of, 
304 ff. 

Logical opposition, 201. 


Major members, of symbolic groups, 
48, 49. 

Materialism, 288. 

Matter, 66, 84. 

Meaning, ch. i (9ff.), 21 ff.; psy- 
chology of, 23 ff., 28, 29;  be- 
havioristic theory of, 25 ff.; habits 
of, 26; syntactical, 31, 35 ff., 39, 
40; the non-existent, 35, 36; of 
complexes, 154, 155; hypostatiza- 
tion of, 158; in perception, 166... 


328 INDEX 


Mediate knowledge, 13 ff., 38. 

Meinong, A., 8, 152. 

Memory, 291, 292, 295. 

Metaphysical insight, 272, 277, 279, 
310 ff. 

Metaphysics, 5 ff., 150, 170, 191, 208; 
of knowledge, ch. viii (266 ff.). 

Mind-body, problem of, 287, 298. 

Mind-isolation, in Locke and Kant, 
Q73 ff. 

Monism, epistemological, 276, 293. 

Moore, G. E., 8, 76, 151-153. 

Multiplicity, of groups, 48, 63. 

Mysticism, 315. 


Negation, ch. vi (197 ff.); negative 
facts, 197 ff., 219; ambiguity of 
negative, 198 ff., 219; as variable, 
199; meaning of, 200; ground of, 
200, 204, 216 ff.; defined through 
truth, 209 ff.; negation and infer- 
ence, 210 ff.; truth and falsity of 
negatives, 212; purely conceptual 
negation, 219; inferential nega- 
tion, 219; double negation, 239, 
240. 

Negatives, 186. 

Nominalism, 67, 86 ff., 106, 129. 

Non-deductive systems, 91. 

Non-Euclidean geometry, 134, 147. 

Non-existent objects, 35, 36, 158; 
reference to, 136 ff., 144, 159. 

Nonsense, 93 ff., 106. 

Null class, 243. 

Number, 46. 


Objectives, 152 ff. 

Objective reference, 153 ff., 192. 

Objectivity, of symbolic forms, 156; 
criteria of, 159. 

Objects, complex, 35; formal char- 
acters of, 43 ff.; identity of, 59; 
relational object, 97; non-existent, 
objects, 35, 36, 158; perceptual 
object, 161, 162, 164, 296 ff. 

Occam’s razor, 237. 

One and Many, The, 141. 

Ontological argument, 158, 159, 182, 
183. 

Operations, 52, 79, 80; perception of, 


88; criterion of, 244, 253 ff.; dis- 
tinguished from relations, 263. 

Opposition, logical, 201. 

Order, 62, 95 ff., 106, 107; of poly- 
adic complexes, 98; postulates for 
serial order, 254, 255 (note). 

Otherness, 203. 


Parameters, 252. 

Parmenides, 207. 

Particularity, 83. 

Passive form, grammatical, 98. 

Peirce, C. S., 314. 

Perception, 32, 34, 66, 133, 159 ff.; 
of numerical diversity, 68; of uni- 
versals, 75 ff.; of operations, 88; 
of relations, 88. 

Perceptual object, 161, 162, 296 ff.; 
reality of, 164. 

Physical objects, 296-298. 

Plato, 36, 66, 81, 107, 189, 273. 

Poincaré, H., 314. 

Positive theory of knowledge, 6 ff., 
86, 269. 

Possibility, for knowledge, 92, 93, 
106. 

Post-Kantians, 273. 

Postulate-sets, 227 ff. 

Presentation, 13, 32, 33; of logical 
forms, 107. 

Presentational thought, 167, 168, 
193. 

Primary and secondary qualities, 
299, 300. 

Principia Mathematica, 51, 108, 114, 
117, 118, 124, 136-141, 229, 230, 
243, 256. : 

Privacy, of objects, 229 (note). 

Proper names, 47, 74, 108, 114, 123 ff., 
129, 144, 146. 

Proposition, 35, 111, 112, 146, 151; 
definition of, 183, 184; asa tertium 
quid, 151 ff.; simple symbols as 
propositions, 183, 184. 

Psychological ambiguity, 119, 120. 

Psychology, of meaning, 23 ff., 28, 29. 

Punctuation, 51. 

Pure awareness, 18, 20, 39, 43, 66, 
157, 305 ff. 

Pythagoreans, 46. 


2 a 


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INDEX 


Qualities, 52,79; distinguished from 
relations, 80 (note); primary and 
secondary, 299, 300. 


Rationalism, 169, 315. 

Realism, 67, 286, 288, 289. 

Reality, 150; of perceptual objects, 
164 ff.; limited concept of, 170, 
193; definition of, 286, 287. 

Recurrence, of symbols, 55 ff. 

Referent, of relations, 98 ff. 

Reflexive expressions, 61, 62, 230, 
wale 

Reflexive relations, 80. 

Reid, T., 16, 161. 

Relations, 45, 52, 79, 80, 100 ff.; 
reflexive, 80; perception of, 88; 
triadic, dyadic, monadic, 104; ex- 
ternality of, 130; internality of, 
130; distinguished from operations, 
245, 253 ff. 

Relativism, 189. 

Relatum, 98 ff. 

Representation, analytical, 31; scale 
of, 47. 

Round-square, The, 136 ff. 

Royce, J., 292. 

Russell, B., 8, 51, 100; theory of 
descriptions, 108 ff., 124 ff., 136, 
145, 161, 175; theory of negation, 
197 ff., 221, 291. 


Scepticism, 166, 187 ff., 268-270. 

Schopenhauer, 164, 165 (note). 

Scientific knowledge, 133 ff. 

Scientific method, as hypothetical, 
270. 

Sensation, 281-283, 307. 

Sensationalism, 164 ff. 

Sense data, 14 ff., 19, 160 ff. 

Serial order, postulates for, 254, 
255 (note). 

Sheffer, H. M., 201, 202. 

Signs, of syntax, 51, 65, 225; of in- 
terpretation, 120 ff. 

Simple symbols, 31 ff., 39, 64, 154; 
form of, 47; as propositions, 183, 
184. 

Simplicity, 202. 

*““Some,”’ 121, 122, 145. 


329 


Sophists, The, 189. 

Space, 69 ff., 105; Euclidean, 134 ff. 

Speech, 149. 

Spencer, H., 268. 

Spinoza, 273, 277, 289, 291, 310; on 
agnosticism, 272. 

Spiritualism, 289. 

Structure, symbolic, 41 ff.; of real- 
ity, 304 ff. 

Subject, of relations, 97. 

Subsistent entities, 151 ff. 

Substance, 44, 128; and quality, in 
Locke, 274. 

Substantives, 89 ff., 117. 

Substitution, 27; deductive, 224, 
226, 227, 228 ff.; completeness of, 
230, 231; interpretation of rules 
of, 250 ff. 

Subsumption, of classes, 240 ff., 247. 

Sufficient reason, 72, 74. 

Symbol, general nature of, 21. 

Symbolic groups, 35 ff., 40. 

Symbolism, general principles of, 225. 

Symmetry, 99 ff. 

Syntactical meaning, 31, 35 ff., 37, 
39, 40. 

Syntax, 40, 41, 106; rules of, 41; 
plans of, 91; of fact, 91; of the 
imagination, 93 ff.; of language, 
93 ff., 102; signs of, 51, 65, 225; 
in formal systems, 224 ff. 

Synthetic judgments, 126 ff., 147. 


Tabula rasa, 34, 38, 167, 283. 

Tautologous symbols, 48, 55 ff., 62, 
63. 

Terms, 82 ff., 105. 

Tests of truth, 174ff., 190, 191, 
194. 

“The,” 120, 145. 

Theory, 172, 173. 

Thing-in-itself, 167, 168, 275, 278. 

Thought, 29, 30, 281-283; and 
action, 28; abstract, 117; presen- 
tational, 167, 168, 193; laws of, 
205 ff.; as symbolic manipulation, 
260, 261. 

Time, 69 ff., 105. 

Totality, as defining concept of 
classes, 141 ff. 


330 


Truth, 91, 92, 148, ch. v (149 ff.); as 

» conceivability, 174 ff.; as con- 

sistency, 174; as correspondence, 
173, 176 ff., 192; coherence theory 
of, 175 ff.; tests of, 174 ff., 190, 
191; value of, 181; ambiguous 
truth, 212 ff. 

Type, of symbolic groups, 47, 48, 63. 


Understanding, 25, 29. 

Unity, of groups, 78 ff.; of facts, 
78 ff., 88; elements of, 52, 53, 65, 
104; complex elements of, 103 ff.; 
symbols of, 89ff.; of mind and 
objects, 294 ff. 

Universals, ch. iii (66 ff.); percep- 
tion of, 75 ff.; identity of, 76 ff.; 


INDEX 


reality of, 85 ff.; descriptions of, 
122; as object of thought-activity, 
303. 

Universal class, 243. 


Validity, conceptual, 223. 

Variables, 73, 114 ff., 146, 223; iden- 
tity of, 118; negative as a variable, 
119 ff.; functional variables dis- 
tinguished from interpretational, 
249 ff.; functional, 263. 


Watson, J. B., 27. 

Whitehead, A.N., 8, 20, 52, 150, 
289 (note), 293. 

Whitman, Walt, 226. 

Willis, G., 33. 





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